Newest questions tagged aliasing - Signal Processing Stack Exchange most recent 30 from dsp.stackexchange.com 2019-07-21T03:36:02Z https://dsp.stackexchange.com/feeds/tag?tagnames=aliasing&sort=newest http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://dsp.stackexchange.com/q/59558 0 Aliased Signal's Frequency hevansa98 https://dsp.stackexchange.com/users/44196 2019-07-16T23:14:43Z 2019-07-16T23:38:06Z <p>So I have an incoming signal of 137.9 MHz and a sampling frequency of 1.4 MHz. Once sampled how do I calculate the aliased signal's new frequency? Bandwidth is 38 kHz with a subcarrier of 2400 Hz if that information is relevant. Just looking for an equation to calculate the aliased frequency.</p> <p>The hardware used is a RTL-SDR into a computer sampling at 1.4 MSPS </p> <p>This is the signal's information page</p> <p><a href="https://www.sigidwiki.com/wiki/Automatic_Picture_Transmission_(APT)" rel="nofollow noreferrer">https://www.sigidwiki.com/wiki/Automatic_Picture_Transmission_(APT)</a></p> https://dsp.stackexchange.com/q/59155 0 Sampling Audio Signal A.haji https://dsp.stackexchange.com/users/43896 2019-06-28T06:20:43Z 2019-06-29T08:18:15Z <p>I generate a 19kHz audio signal with sampling frequency of 44100 using Matlab. Due to the sampling, some other frequencies are generated in addition to the 19 kHz signal. When I play this audio, I hear additional voices. How I can remove these additional sides? I think it needs aliasing filtering, but I cannot filter signal after DAC, because I generate the audio signal and play it with phone or computer, I cannot put any filter after A/D. </p> https://dsp.stackexchange.com/q/58611 1 Calculate aliasing of $x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$ when sampled with $F_s = 1000$ IdiotWithNoShame https://dsp.stackexchange.com/users/43457 2019-05-30T17:51:06Z 2019-05-30T20:15:35Z <p>I'm asked to sample the signal <span class="math-container">$$x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$$</span> with sampling frequency <span class="math-container">$F_s = 1000$</span> and plot the magnitude spectrum for the resulting sampled signal. </p> <p>My thinking is that the frequency of <span class="math-container">$300$</span> does not change, so it just results in the normalized frequency <span class="math-container">$\frac{3}{10} = 0.3$</span>.</p> <p>Since <span class="math-container">$600$</span> is above the nyquist frequency, aliasing arises. So we get the frequencies <span class="math-container">$\frac{6}{10} = 0.6$</span> and <span class="math-container">$\frac{6}{10} - 1 = - 0.4.$</span></p> <p>So in total I would plot peaks at the frequencies <span class="math-container">$\pm0.3, \pm0.4, \pm0.6$</span>, but the answer is supposedly: </p> <p><a href="https://i.stack.imgur.com/K2o7C.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/K2o7C.png" alt="enter image description here"></a> </p> <p>Why? Where is my thinking wrong? And what is the method to always get the right aliasing peaks?</p> https://dsp.stackexchange.com/q/58476 0 Aliasing from downsampling and Nyquist Anton B https://dsp.stackexchange.com/users/31545 2019-05-22T13:06:37Z 2019-05-22T14:51:54Z <p>In a book Conceptual Wavelets in Digital Signal Processing by Lee Fugal 2009 on page 246 the author talks about aliasing present in DWT subbands due to downsampling by 2 and states:</p> <blockquote> <p>Recall from DSP that for a signal at 0.3 Nyquist aliasing from downsampling will "reflect" the signal across Nyquist. Thus we see the aliasing components at Nyquist minus 0.3 Nyquist or 0.7 Nyquist.</p> </blockquote> <p>I thought it was safe to downsample a signal below 0.5 Nyquist by 2, isn't that correct ? Also on the image below the signal at 0.3 Nyquist and the alias at 0.7 Nyquist have different amplitudes.</p> <p><a href="https://i.stack.imgur.com/LlB6z.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/LlB6z.png" alt="enter image description here"></a></p> <p>I would think the aliasing in approximations can only occur because of imperfect filtering i.e. because some of the high frequencies above 0.5 Nyquist were also captured before downsampling by 2. But the author also shows using UDWT ( undecimated DWT ) with the same filters that without downsampling approximations after filtering have only frequencies around 0.3 Nyquist:</p> <p><a href="https://i.stack.imgur.com/Vshdg.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Vshdg.png" alt="enter image description here"></a></p> <p>So where does aliasing come from in DWT in this example?</p> https://dsp.stackexchange.com/q/56249 3 Understading sampling theorem and aliasing Niousha https://dsp.stackexchange.com/users/38776 2019-03-26T20:44:47Z 2019-03-27T13:45:31Z <p>A real-valued analog signal with a flat spectrum between f = 0 Hz, and fmax is sampled at a sampling frequency fs = 24 kHz. The sampled signal is then processed with an ideal lowpass filter with cutoff frequency = 0.25pi.</p> <p>How can we specify the range for omega in which aliasing can be torelated and also determine the maximum signal frequency fmax of the analog signal such that no aliasing components are present in the filter output? </p> https://dsp.stackexchange.com/q/55598 0 Amplitude Response at greater than half the sampling frequency Darklink9110 https://dsp.stackexchange.com/users/18743 2019-02-22T03:45:09Z 2019-02-22T04:20:20Z <p>I am hoping to clear up some confusion I have. In a lab I am taking, we analyzed the amplitude response of a simple system. We found that as we increased the input signal frequency to greater than half the sampling frequency, the output signal began to flat line. The picture below show the corresponding Amplitude Response. </p> <p><a href="https://i.stack.imgur.com/rGmzu.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/rGmzu.png" alt="Amplitude Response for a system with a sampling rate of 16kHz"></a></p> <p>I am aware of the Nyquist theorem, and I thought that the reason the output signal flatlined at frequencies greater than 8 kHz was because the sampling frequency was 16 kHz. </p> <p>But during a second experiment of generating a sine wave, I discovered the concept of folding about the Nyquist frequency. Now in this case, increasing the generated signal frequency to greater than the Nyquist frequency caused the output signal to not decrease in amplitude, but to become symmetric about the Nyquist frequency.</p> <p>E.g.</p> <p>Generating a sine wave of 14 kHz produced an output of a sine wave of 2 kHz.</p> <p>How are these two concepts related? It seems in the first example, going above the Nyquist frequency caused the output signal to flatline. In the other case, generating a signal above the Nyquist frequency didnt cause the output to flatline, but caused the output signal to only have a different output frequency. </p> https://dsp.stackexchange.com/q/55563 0 Minimum sample frequency that allows reconstruction of information signal but VIOLATES Nyquist? Mike_1234321 https://dsp.stackexchange.com/users/40688 2019-02-20T15:45:16Z 2019-02-20T15:45:16Z <p>Say in the frequency spectrum, you have an information signal between (-100, 100) Hz, and a noise signal between (-700, -500) and between (500, 700) Hz. What is the minimum possible sample frequency that allows reconstruction of the information signal without distortion? Any ideal filter can be used. </p> <p>At first I thought Fs = 400 Hz. But when plotting this out in the frequency domain, I believe aliasing will occur if the noise signal has non-zero components at say -700 or -500 Hz. When Fs = 800 Hz, the same phenomen occurs. But When Fs = 800 + 0.00000001 (some really small number), the potential for aliasing is zero if an ideal low-pass filter is used. Am I right in my reasoning?</p> https://dsp.stackexchange.com/q/55053 0 Sample-rate, filtering, digital-filtering and aliasing Biologichael https://dsp.stackexchange.com/users/40195 2019-01-24T12:00:10Z 2019-06-25T04:04:25Z <p>I am strugling with a question that I hope someone can help me with.</p> <p>I am recording single molecule events which I detect is picoampere square deflections.</p> <p>I wish to use as gentle low-pass bessel filtering as possible.</p> <p>The lowest filter settings my amplifier allow are 10 kHz and 100 kHz, and my digitizer have a maximal sampling rate of 500 kHz. I am afraid of corrupting my signal to much, but do not have the intuitive understanding of sampling and filtering to know if I am doing something wrong. Here is what I do:</p> <p>I filter the signal with a 100 kHz bessel filter and digitize it with a 500 kHz sampling rate. I then wish to filter my digitized data with a 35 kHz digital filter.</p> <p>Would this mess up my data? I hear people say that I am on safe ground if i sample at appropximatly 10x my filter settings, but I get to this 'safe zone' only when I do the post-sampling digital filtering. So I guess what I realy do not understand is if the order of filtering, sampling, filtering does something nasty to the data.</p> <p>I hope I was able to communicate my question clear enough.</p> <p>Thank you very much, Best regards, Michael</p> https://dsp.stackexchange.com/q/54546 0 What does the frequency band mean when it comes to finding aliases? Sam B https://dsp.stackexchange.com/users/39814 2019-01-01T18:55:33Z 2019-07-02T16:01:50Z <p>The time signal which i'm trying to find the aliases for is: </p> <p><span class="math-container">$$x:{\mathbb R}\rightarrow {\mathbb R}\\\ x(t)=\cos(50t) +2\cos(70t).$$</span></p> <p>If the sample period is <span class="math-container">$T_s = \frac{\pi}{60}$</span> then according to Nyquist -Shannon sampling theorem (which btw my professor failed to prove) there is/are a signal(s) which after sampling will be equal to the sampled version of the above signal, if we sample those with the same sample frequency in the frequency band <span class="math-container">$[-55, 55]$</span>.</p> <p>I don't understand the meaning of the last sentence , what does a frequency band means here? </p> https://dsp.stackexchange.com/q/53998 0 Choosing a Sampling Rate and a Cutoff frequency Andrea G https://dsp.stackexchange.com/users/39393 2018-12-08T23:25:29Z 2019-05-08T01:01:55Z <p>I have an assignment:</p> <blockquote> <p>You wish to generate a pure 1000 Hz tone digitally using a computer. How would you choose a sample rate that assures that you could generate the tone and use the same sample rate to generate a 20 kHz tone? Specify the corner frequency and slope of the filter would you need to assure that the tone is as close to perfectly pure as possible?</p> </blockquote> <p>My current thought is to sample at 10 kHz because that is well above the Nyquist rate for the 1000 Hz tone and then the first harmonic would be at 20 kHz. I assume I would then need a steeply sloping Chebyshev filter that cuts off just above 20 kHz? Am I on the right track?</p> https://dsp.stackexchange.com/q/53605 0 Nyquist Theorem adding two same frequency near to Nyquist Frequency with phase shift kaankaan https://dsp.stackexchange.com/users/39076 2018-11-24T21:02:21Z 2019-04-24T04:06:06Z <p>This is my first question on this platform. Sorry if I made mistakes.</p> <p>What happens if we add two or more same frequency signals near to Nyquist Frequency with phase shift and sample them?</p> <p>For example, assume that we have a signal of 18000Hz. And add another signal with same frequency, but having 180 degree phase with our first signal. Then, sample this total signal at 36000Hz. What happens if we reconstruct this signal? Does this situation result in aliasing?</p> <p>Note: I'am trying to figure out how exactly sound records are sampled when musicians playing their instruments. For example, assume that two keyboard players playing a note at 20000Hz which will be sampled at 44100Hz. Since they are human-being they are not supposed to hold the rhythm like in electronic music. Therefore, there will be a phase shift in their playing and wouldn't this cause aliasing in reconstructed signal?</p> <p>Thanks for the answers.</p> https://dsp.stackexchange.com/q/51707 1 Downsampling impact on complex phase AFC45 https://dsp.stackexchange.com/users/37503 2018-09-03T10:07:04Z 2018-09-03T10:48:59Z <p>For my application, I have to downsample a bandpass complex signal which spectrum is located on the second Nyquist zone. Knowing that this processing will cause a spectrum inversion, what would be the additional side effects (SNR reduction, less amplitude ..) ? Will the phase's linearity be conserved (supposing that the pass-band anti aliasing filter has a linear phase) ? Does anyone have a reference detailing those side effects of the downsampling ? Thanks for any help. Mourad.F</p> https://dsp.stackexchange.com/q/51533 2 Alias-free digital nonlinear filter design Mike Battaglia https://dsp.stackexchange.com/users/18276 2018-08-27T03:30:47Z 2018-08-28T02:47:53Z <p>@Jazzmaniac has a good answer to the question of how to design an alias-free digital nonlinear time-invariant filter here: <a href="https://dsp.stackexchange.com/a/28787/18276">https://dsp.stackexchange.com/a/28787/18276</a></p> <p>Basically, according to that answer, a digital nonlinear time-invariant filter is alias free if and only if it commutes with subsample translations. Meaning that it doesn't matter whether you filter and then translate, or translate and then filter. Sinc interpolation is required for perfect subsample translations, but of course you can always use a finite interpolator that is good enough.</p> <p>This question is to elaborate:</p> <ol> <li><p>How can we see the link between subsample translation invariance and aliasing?</p></li> <li><p>Is there any easy way to see what these filters look like?</p></li> <li><p>Do the filters have some standard form they can be put in?</p></li> <li><p>Do we know what the alias-free version of the monomials look like? (i.e. the alias-free version of $y[t]=x[t]^n$ for some positive natural number $n$)</p></li> <li><p>Are there any good references or published works on the topic of alias-free nonlinear filter design?</p></li> </ol> https://dsp.stackexchange.com/q/51225 1 Decimation Aliasing Ronnie https://dsp.stackexchange.com/users/37213 2018-08-14T06:27:39Z 2018-08-14T20:51:28Z <p>Lets say you have a signal which is sampled at rate $f_s$ and the bandwidth after sampling is $B$.</p> <p>Now you want to decimate this signal with a new sample rate $f_{s, new}$ where $f_{s, new} &lt; f_s$ and you also are only interested in preserving bandwidth $B'$ where $B' &lt; B$. Also $f_{s, new}$ > $2B$' and $f_{s, new}$ &lt; $B'$</p> <p>Is there a way to calculate the band of frequencies that will be aliased to the band of interest i.e. from $-B'$ to $B'$</p> https://dsp.stackexchange.com/q/50714 1 Designing an experiment to show blue noise not adding noise below nyquist and not aliasing above Alan Wolfe https://dsp.stackexchange.com/users/15130 2018-07-21T17:47:17Z 2018-07-22T02:39:32Z <p>I read this paper from 1983 "<a href="https://cloudfront.escholarship.org/dist/prd/content/qt0qq9b8zx/qt0qq9b8zx.pdf?t=nvz1sw&amp;nosplash=dce32581f54a3da1d0ad2891af0b4561" rel="nofollow noreferrer">Spectral Consequences of Photoreceptor Sampling in the Rhesus Retina</a>".</p> <p>This paper talks about blue noise sampling patterns in the retina and says that:</p> <blockquote> <p>The results (Fig. I) indicate that throughout the retina the cones provide a novel form of optimal spatial sampling: optimal in the sense that minimal noise is introduced for spatial frequencies below the nominal Nyquist limits implied by local receptor densities (the limits that would obtain if the cones formed a regular lattice), while spatial frequencies above the local Nyquist limits are not aliased back into conspicuous moire patterns but instead are scattered into broadband noise. Thus, the visual system avoids the aliasing distortion of high frequencies inherent in any regular arrangement of image sampling elements and simultaneously minimizes sampling noise for low frequencies that fall within its potential Nyquist bandwidths. These advantages stem from a quasi-random (that is, random but not Poisson) spatial sampling scheme that apparently has not been used in man-made image-recording devices.</p> </blockquote> <p>I take that to mean that blue noise:</p> <ol> <li>Doesn't add (much) noise when sampling frequencies below nyquist.</li> <li>Doesn't alias for frequencies above nyquist.</li> </ol> <p>This is in contrast to:</p> <ol> <li>Uniform sampling which doesn't add noise to any frequency, but aliases frequencies above nyquist.</li> <li>White noise (uniform random) sampling, which adds noise to all frequencies, but doesn't alias for frequencies above nyquist.</li> </ol> <p>That makes sense, but now I'm trying to think of how I could make a simple experiment to show this being true - preferably in the context of 2d sampling and 2d images (image processing / image sampling), but 1d would be ok too.</p> <p>I get that I could use blue noise to sample sine waves of varying frequencies but am unsure how exactly that sampling would work.</p> <p>I know how to generate blue noise sample points in any dimension using <a href="https://blog.demofox.org/2017/10/20/generating-blue-noise-sample-points-with-mitchells-best-candidate-algorithm/" rel="nofollow noreferrer">Mitchel's best candidate algorithm</a>.</p> <p>I'm guessing I would generate N sample points and then do a reconstruction filter on those sample points, but thinking about that, I can't see how noise would present itself (although, aliasing would just be "missed frequencies"), and frankly I'm not real sure how to do a decent reconstruction filter.</p> <p>Am I on the right track for making a decent but simple experiment to show these statements being true empirically? Or should I be doing something different?</p> https://dsp.stackexchange.com/q/48742 0 Accelerometer BMI160 changing bias Gaussiano https://dsp.stackexchange.com/users/31691 2018-04-24T13:30:28Z 2019-05-09T20:03:00Z <p>Goal: Obtain the 3-axis accelerations from the Bosch BMI160 IMU when measuring the accelerations of the bogie of a commercial train. The accelerometer used is installed in a PCB and used by an mbed microcontroller. The mbed manages to receive and save the data from the accelerometer at 50 Hz. The BMI160 has some options such as measurement range that can be changed: to avoid sensor saturation the limit is set to ±4g.</p> <p>Issue: The Z-acceleration (gravity-like oriented) shows an important bias due to unknown reasons. Phenomenon in Figure 1 and 2:</p> <p><img src="https://imgur.com/k341e2T.jpg" alt="Figure 1"></p> <p><img src="https://imgur.com/gvMAbXL.jpg" alt="Figure 2"></p> <p>The odd phenomenon can be more easily seen in this picture of the zoom Z-acceleration:</p> <p><img src="https://i.imgur.com/1PjdCJ7.png" alt="Figure 2.zoom"></p> <p><img src="https://i.imgur.com/FY314M8.png" alt="Figure 2.zoomzoom"></p> <p>time stamps and $Acc_z$ data can be found here: <a href="https://pastebin.com/raw/4PyAtVU8" rel="nofollow noreferrer">https://pastebin.com/raw/4PyAtVU8</a></p> <p>It can be seen on it, that the average of that signal is not the gravity value. If it where due to the rotation of the object, a similar effect shall be seen in the other axis. Anyway, this does not seem to be the case, as the vehicle is a railway going forward.</p> <p>If we calculate the low-pass-filtered signal ($f_cut = 0.1\ Hz$), the signal is clearly non-oscillating. The expected result should be something more similar to what is shown in purple in the next figure:</p> <p><img src="https://i.imgur.com/3qAoRnU.png" alt="Filtered signal"></p> <p>Moreover, if we zoom in the last part of the signal, we can see that there are not any particular trends:</p> <p><img src="https://i.imgur.com/p17T6Pw.png" alt="Filtered signal zoomed"></p> <p>Question: Why the bias of the acceleration, which should be a slow-changing as a random variable, causes such a distorsion on the signal? It seems to affect only to big accelerations caused by impacts.</p> <p>In next figure, you can see more information about the device layout:</p> <p><img src="https://i.imgur.com/NzLzF3Q.jpg" alt="Layout"></p> <p>The accelerometer (green component) is well fixed to the PCB with strong adhesives. The PCB itself is screwed to some wooden pieces which are also strongly sticked to the plastic box.</p> <p>The whole device is fixed to the train through duck tape using metal plates for the contact. All componentes are strongly fixed one to each other and we have not observed any relative bouncing between components. The next figure shows the set up:</p> <p><img src="https://i.imgur.com/AMy9FtA.png" alt="Vehicle axis"></p> <p>The blue axis are the vehicle reference system and, as it can be stated with the sign of gravity value, it does not coincide with the accelerometer axis.</p> <p>I think the phenomenon may be due to an aliasing issue or just a problem with this low-cost accelerometer. Any insight from anybody?</p> https://dsp.stackexchange.com/q/48289 0 What does it mean that the DFT equals the Complex Fourier Coefficients for even frequencies? user3002473 https://dsp.stackexchange.com/users/15316 2018-04-03T20:51:53Z 2018-04-09T05:12:10Z <p>I have a periodic signal, with period $1$</p> <p>$$x(t) = \begin{cases} 1 \qquad &amp; 0 \le t - \lfloor t \rfloor &lt; \tfrac12 \\ 0 \qquad &amp; \tfrac12 \le t - \lfloor t \rfloor &lt; 1 \\ \end{cases}$$</p> <p>$\lfloor t \rfloor = \operatorname{floor}(t)$ is the <code>floor()</code> function, returning the largest integer no greater than the argument $t$.</p> <p>$$x(t+1) = x(t) \qquad \forall t \in \mathbb{R}$$</p> <p>The complex Fourier series for $x(t)$ is</p> <p>$$x(t) = \sum\limits_{k=-\infty}^{\infty} c_k \ e^{i 2 \pi k t}$$</p> <p>The complex Fourier coefficients are</p> <p>\begin{align} c_k &amp;= \int_{-1/2}^{1/2} x(t) \ e^{-i2\pi k t} \ \mathrm{d}t \qquad \qquad k \in \mathbb{Z} \\ &amp;= \int_{0}^{1/2} 1 \ e^{-i2\pi k t} \ \mathrm{d}t \\ &amp;= \tfrac{1}{-i2\pi k } \big( e^{-i\pi k} - 1 \big) \\ &amp;= \tfrac{i}{2\pi k } \big( (-1)^k - 1 \big) \\ \end{align}</p> <p>and are $0$ for even $k$.</p> <p>Now, we sample $x(t)$ at $N\in 2\mathbb{N}$ time values, </p> <p>\begin{align} x[n] &amp;= x(t_n) \\ &amp;= x\left(\tfrac{1}{N}n\right) \end{align} </p> <p>where $\tfrac{1}{N}$ is the sampling period, $N$ is the sampling frequency, and $t_n = \frac{n}{N}$, with $n=0, N-1$.</p> <p>Let $X[k]$ denote the DFT of this finite sequence $x[n]$.</p> <p>$$X[k] = \sum\limits_{n=0}^{N-1} x[n] \ e^{-i2\pi nk/N}$$</p> <p>One can show that $X[k] = 0$ for even $k$ as well, so $X[2k] = c_{2k}$, but $X[2k+1] \neq c_{2k+1}$.</p> <p>I'm trying to come up with an intuitive explanation as to why $X[2k] = c_{2k}$, but $X[2k+1]\neq c_{2k+1}$. Obviously, we shouldn't really expect them to be equal in general since $X[k]$ is really just a Riemann sum approximation to $c_k$ with $N$ intervals, but in this case it seems there may be an explanation, since $X[2k] = c_{2k}$.</p> <p>So far, all I can come up with is that since $x(t)$ isn't bandlimited, the DFT of the discrete sample of $x(t)$ is essentially trying to "fit" a bandlimited signal to the samples $x[n]$, and so for some reason this doesn't have any content at frequencies $2\pi (2k) = 4\pi k$ for any $k\in\mathbb{N}$.</p> <p>Is there any specific reason for this? From the above argument, I have a feeling it has to do with aliasing, but I can't exactly make the connection.</p> https://dsp.stackexchange.com/q/48117 0 Frequency of a single sample in a digital signal and aliasing user17127 https://dsp.stackexchange.com/users/0 2018-03-26T16:33:09Z 2018-03-27T04:57:12Z <p>I'm involved with digital audio synthesis. I know that if I create a raw non band-limited waveform it would contain frequencies above Nyquist thus violating the Nyquist Shannon theorem and the signal will contain aliased components. So I wonder if I can also create aliasing by other means, like a "click" from a fast envelope or a single sample in a digital stream. So what is the frequency of a single sample (is it sample rate/1 ?) and does such clicks alias in the frequency domain? </p> https://dsp.stackexchange.com/q/48112 0 What happens if an harmonic in a band-limited signal at Nyquist frequency is added to a 90 degrees out-of-phase replica of it? user17127 https://dsp.stackexchange.com/users/0 2018-03-26T15:36:53Z 2018-03-26T15:48:42Z <p>I'm interested about aliasing in digital audio and I wonder if aliasing can be produced by simple mixing of band-limited signals. As I know a band limited signal can contain frequencies up to sample rate/2 frequency, the so-called Nyquist frequency. Is this right?<br> If that is so, what will happen if an harmonic in a band-limited signal at Nyquist frequency is added to a 90 degrees out-of-phase replica of it? Will this create an harmonic with double frequency and could such an addition create aliasing? </p> https://dsp.stackexchange.com/q/47988 6 Can addition of two band limited signals create aliasing? user17127 https://dsp.stackexchange.com/users/0 2018-03-21T00:34:03Z 2018-03-21T10:50:53Z <p>Can mixing/adding two band-limited signals create any frequencies above Nyquist?</p> https://dsp.stackexchange.com/q/47510 0 low frequency transform arash https://dsp.stackexchange.com/users/34188 2018-03-01T08:09:54Z 2018-03-01T18:47:05Z <p>I was wondering which type of signals have bounded-support Fourier transform. e.g. their transform is limited from zero to some non-infinite frequency. </p> <p>The main reason I'm into it is that in Shannon's sampling theorem, we know that for some sampling rate, reconstruction is possible without aliasing, but I guess that's only true for functions which have a limited (cut-off) frequency </p> https://dsp.stackexchange.com/q/46965 0 Determine minimum sample rate for continuous sinusoid Sid https://dsp.stackexchange.com/users/28503 2018-02-05T02:34:20Z 2018-02-05T06:35:09Z <p>Consider a signal $$x(t) = \cos(175\pi t)$$ which is sampled to produce discrete time signal $$x[n] = x(nT_s)$$ The fundamental period of $x[n]$ is $$N_0 = 7$$</p> <p>Given this, what is the smallest possible sample rate $T_s$? (Ans: 1.6327 ms).</p> <p>I would assume that this is related to finding the Nyquist frequency. I was thinking:</p> <p>Since, $$N_0 = 7 \implies f_0 = \frac17 \implies f_{\mathrm{Nyquist}} = 2 \frac17\implies T_s = \frac72$$ However, this is obviously incorrect. I am not even using any information of the original signal. Any suggestions on what I could be doing wrong here?</p> https://dsp.stackexchange.com/q/46562 0 What happens on signal during aliasing? Alena https://dsp.stackexchange.com/users/31543 2018-01-20T12:36:10Z 2018-01-21T00:09:06Z <p>So I have signal with frequency of $15Hz$ and sample rate frequency is $20Hz$.</p> <p>What happens if we sample the signal at a frequency that is lower that the Nyquist rate? We will have aliasing. Sample rate frequency should be at least bigger than $2*f_{max}$.</p> <p>I understand that part but I'm confused how that will look like. Can someone help me with that?</p> https://dsp.stackexchange.com/q/45697 1 Band Limited Impulse Train - DC offset correction lemko2 https://dsp.stackexchange.com/users/32601 2017-12-09T14:23:10Z 2017-12-10T15:42:50Z <p>I am trying to get band limited saw-tooth wave. I have found this paper: <a href="https://ccrma.stanford.edu/~stilti/papers/blit.pdf" rel="nofollow noreferrer">Alias-Free Digital Synthesis of Classic Analog Waveforms</a>.</p> <p>I am prototyping this code in common LISP, here is snippet of what I wrote: <a href="https://pastebin.com/Ny4L0EH5" rel="nofollow noreferrer">https://pastebin.com/Ny4L0EH5</a></p> <p>I managed to get something that in time domain looks like sawtooth but it has rising DC offset that causes output to approach infinity (this is generated by <code>blit</code> function).</p> <p>I read that I should fix this with one pole high-pass filter. I have put simple IIR but without any good results. It makes sense for me to remove this DC bias this way since it is digital equivalent of RC differentiating circuit that block DC bias.</p> <p>I have tried a few different sets of coefficients but without any good results.</p> <p>I have looked hard with both duckduckgo and google for any information about DC offset correction in this method but i did not managed to find anything.</p> <p>I have also tried to subtract from output sample average value of one period but again no luck.</p> <p>I have saved to file band limited version of Dirac comb and tried to filter it with low pass filter in octave but it does not change time domain shape of data in any way, only amplitude decreases. I tried this because I read about this way of performing summation.</p> https://dsp.stackexchange.com/q/45090 1 Understanding the mathematical proof for the alias frequencies in a sampled sine wave IanR https://dsp.stackexchange.com/users/31571 2017-11-11T20:02:14Z 2017-11-12T19:33:23Z <p>I'm struggling to get my head round the mathematical proof for the alias frequencies in a sampled sine wave.</p> <p>I understand that sampling a sine wave of frequency $f_0$ every $t_s$ seconds gives you:</p> <p>$$x[n]=\sin(2\pi f_0nt_s)$$</p> <p>I also understand that, because the sine wave is periodic every $2\pi$, you can add any multiple of $2\pi$ to the angle and get the same values for the sine, i.e.,</p> <p>$$\sin(2\pi f_0nt_s)=\sin(2\pi f_0nt_s+2\pi m) \quad\text{(where m is any integer).}$$</p> <p>The proof I'm looking at then factors out $2\pi$ and $nt_s$ to get:</p> <p>$$\sin\left(2\pi(f_0+\frac{m}{nt_s})nt_s\right)$$</p> <p>...but then it says to let $m$ be an integer multiple of $n$ so we can replace the $\frac{m}{n}$ ratio with an integer $k$.</p> <p>I don't understand how $m$ can go from being <em>"any integer"</em> to <em>"an integer multiple of $n$"</em>. If $m$ is any integer and $n$ is an integer then how can the ratio between them be an integer?</p> <p>I know I'm missing something obvious here and I'm searching for that light-bulb moment but it's not happening. Because this is so fundamental to DSP I don't just want to accept the formula and move on without thoroughly understanding it.</p> https://dsp.stackexchange.com/q/45071 2 Avoid Aliasing when filming a moving car xava https://dsp.stackexchange.com/users/31902 2017-11-10T11:27:15Z 2017-11-10T19:33:13Z <p>I want to film a moving car with a rolling circumference: 190,5 cm and wheel circumference: 60 cm and 5 spokes.</p> <p>I record with 24Hz. What can be the maximal speed of the car to avoid aliasing?</p> https://dsp.stackexchange.com/q/44254 1 Circular convolution of length L of sequences of length greater than L VMMF https://dsp.stackexchange.com/users/17077 2017-10-09T15:16:33Z 2017-10-10T15:13:18Z <p>I'm trying to understand how may I obtain the circular convolution of length L when the sequences I'm trying to convolve are of length greater than L. </p> <p>For instance this Matlab code using sequences of length 5:</p> <pre><code>c = cconv([0,0.5,1,1,0.5],[0,0.5,1,1,0.5],4); </code></pre> <p>yields a 4 point sequence</p> <pre><code>2.25 2.5 2.25 2.0 </code></pre> <p>and this Matlab code </p> <p><code>cconv([0,0.5,1,1,0.5],[0,0.5,1,1,0.5],3)</code></p> <p>yields a 3 point sequence</p> <pre><code>3 3 3 </code></pre> <p>I know that circular convolution may be seen as linear convolution with aliasing and that if I perform the linear convolution and build overlapping periods spaced every N samples I will get the N point circular convolution but is there a way to obtain circular convolution without having to compute first linear convolution? I'm thinking about the classical way of doing convolution, where I flip one of the sequences in time and shift it and for every shift I multiply the 2 sequences and add to obtain the output sample for that shift</p> https://dsp.stackexchange.com/q/43318 2 Aliasing due to the Convolution of Gaussian Functions omehoque https://dsp.stackexchange.com/users/30463 2017-08-24T20:10:38Z 2018-02-21T00:12:32Z <p>For two discrete-time sequences $f[n]$ and $g[n]$, their linear convolution $(f*g)[n]$ is also given by $$f*g = \mathcal{F}^{-1}(\mathcal{F}(f) \cdot \mathcal{F}(g)),$$ where $\mathcal{F}$ and $\mathcal{F}^{-1}$ denote the DTFT (discrete time Fourier transform) and IDTFT (inverse discrete-time Fourier transform) respectively.</p> <p>Let us consider two Gaussian sequences $f[k]$ and $g[k]$ in the momentum space and we want to convolve them using the formula above. </p> <pre><code>import numpy as np import matplotlib.pyplot as plt L = 17.5 N = 48 dx = L/N dk = 2*np.pi/L x = np.arange(N)*dx - L/2 k = 2*np.pi * np.fft.fftfreq(N, dx) alpha = 1 beta = 1 def f(k): return np.sqrt(np.pi/alpha) * np.exp(-k**2/(4*alpha)) def g(k): return np.sqrt(np.pi/beta) * np.exp(-k**2/(4*beta)) fs = np.array([f(k_) for k_ in k]) gs = np.array([g(k_) for k_ in k]) fftconvfg = np.fft.ifft(fs * gs) plt.plot(ks, np.fft.fftshift(fftconvfg)) </code></pre> <p>I get the following plot. <a href="https://i.stack.imgur.com/hDQLp.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/hDQLp.png" alt="enter image description here"></a></p> <p><strong>Question</strong></p> <p>How can I demonstrate that my plotting is (or, is not) subject to the aliasing artifacts? And if there are aliasing artifacts, how can I get rid of it? </p> https://dsp.stackexchange.com/q/43252 0 Aliasing in digital communication system Tilen Kavčič https://dsp.stackexchange.com/users/30399 2017-08-21T15:13:03Z 2017-08-21T21:48:33Z <p>In a digital communication system, is it possible to counteract the aliasing problem by properly tuning the constellation order $M$ and/or the carrier frequency?</p> <p>Here is my train of thought, please correct me if I'm wrong:</p> <p>The sampling rate needs to be 2 times the signal bandwidth. This is because we need to cover all the frequencies in which the signal operates. If the signal breaks the Nyquist criterion we'll only get a part of the signal. So if I look at a fix sampling rate and try to tune the constellation order $M$ up and down it won't help, because the signal will still have the same bandwidth. The only thing that will change is the transfer rate $r_b = \log_2(M)/T_s$, where $T_s$ is the sampling rate. Also tinkering around with carrier frequency will only move the signal up or down the frequency. So neither of these solutions will counteract the aliasing problem. The only solution is to somehow reduce the signal bandwidth. I'm thinking of using an RRC filter on the transmitter (to shrink the bandwidth) and then using another RRC filter on the receiver to counteract the ISI.</p> https://dsp.stackexchange.com/q/42483 1 What does it mean that one frequency aliases another? Schimay https://dsp.stackexchange.com/users/29784 2017-07-17T19:01:57Z 2017-07-18T04:43:31Z <p>So I was watching a video on sampling and the professor asked which frequencies will alias to 0 and which to $B$ if we are sampling at frequency $f_{s1}$. What does mean that two frequencies alias each other ? </p> <p>The answer is that $0, f_{s1},2f_{s1},3f_{s1},\ldots, nf_{s1}$ will alias to 0 and $f_{s1}+B, 2f_{s1}+B, \ldots, nf_{s1} + B$ will alias to $B$.</p> <p>Could anyone explain this please? The image shows the frequency spectrum in question.</p> <p><a href="https://i.stack.imgur.com/ZpgpB.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ZpgpB.png" alt="enter image description here"></a></p>