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Is it possible to combine decimation and low pass filtering in one step? Not necessarily only for images but also for general signals. Yes, that's what people usually do when they implement downsampling: since of the output of the anti-aliasing filter, you throw away N-1 samples, why even calculate these? The trick is to decompose your filter into polyphase ...


5

No. The aliased component will interfere with the non-aliased components and the interference can constructive or destructive. Trivial example: $$x[n] = \sin\left(\frac\pi2n\right)$$ If you down sample this to $y[n] = x[2n]$, you get all zeros.


4

Absolutely positively -- uh -- maybe. It depends entirely on the underlying process that generated the original series, what the series "means", how much unique information is actually present in those ten samples, how much you're willing to throw away, and what you know about how that information is structured. At the extreme "no" end ...


3

Interpolation in Frequency (DFT Domain) The implementation is well known. In MATLAB it will be something like: if(numSamplesO > numSamples) % Upsample halfNSamples = numSamples / 2; if(mod(numSamples, 2) ~= 0) % Odd number of samples vXDftInt = interpFactor * [vXDft(1:ceil(halfNSamples)); zeros(numSamplesO - numSamples, 1, 'like', ...


2

There is no image problem related to carrier offsets. Image issues are the result of quadrature and ampitude imbalance. Also, the graphic doesn't look correct to me, as a Zero-IF receiver would translate both $f_c +\Delta f$ and $f_c -\Delta f$ to baseband without overlap. It appears the OP may be confusing an image reject down-converter with a zero-IF ...


2

Having images of a signal is very different from having a frequency offset in the signal. Having an image means the signal spectrum is replicated at two or more places.Having a frequency offset in a signal means the spectrum is just shifted in frequency. First let us look at it from the point of view of the innocent receiver who does not know that such a ...


2

The whole point of aliasing and the sampling theoreme is that you cannot (generally) know what an aliased signal was, as you cannot represent infinite bandwidth using finite infornation. If you have extra knowledge of the input signal (eg that DC is not possible, then you might deduce what a string of 1-1-1 was originally.


2

How do I generate a smaller DFT result? that primarily depends on what you want to do with the result and what your specific requirements are Currently, I transform the entire signal and then downsample the result. It would probably better to do a STFT (Short Time Fourier Transform). Pick a frequency resolution that you need and the associated FFT size, ...


2

One potential option would be to split the lowpass filter into the FIR part and the pureley recursive IIR part. $$H(z) = H_1(z) \cdot H_2(z) = \frac{1}{1 - a1z^{-1} - a2z^{-2} - a3z^{-3} - a4z^{-4}} \cdot \left [ b0 + b1z^{-1} + b2z^{-2} + b3z^{-3} + + b4z^{-4} \right ]$$ You still have to apply the recursive part to each sample in the upsampled domain, but ...


2

I am doing something similar to your application with 1D CNN. I think scipy.resample_poly is the most versatile function since it allows both upsampling, downsampling, or a combination of both. Also your comment about "values beyond the boundary of the signal to be zero" can be solved by using the option "line" in padtype, as shown in the function ...


2

The spectrum appears to be the noise-shaping associated with Delta-Sigma Modulation. Specifically we see that the noise increase follows a 20 dB/decade slope, indicative of a first-order delta-sigma modulator. The high end of the noise rolls off consistent with the high frequency roll-off of the filter applied. Below are some charts I have explaining the ...


2

With typical sampling (not noise shaped) you get half a bit for every halving of the sampling rate (with proper filtering of the out of band noise prior to downsampling). So a decimate by two for example consists of a half band filter followed by a down-sample by two which is done simply by selecting every other sample. Assuming white noise, the half band ...


1

$G_0(e^{j\omega})$ and $H_0(e^{j\omega})$ are ideal low pass filters with passband $[0,\pi/2]$ and stopband $[\pi/2,\pi]$. $G_1(e^{j\omega})$ and $H_1(e^{j\omega})$ are ideal high pass filters that are complementary to the lowpass filters, i.e., their passbands coincide with the lowpass filters' stopbands and vice versa. Note that shifting the frequency axis ...


1

This is what happens when a signal is downsampled: you get a scaling of the frequency axis and the addition of shifted spectra (aliasing). The same happens to the lowpass filtered signal. The spectrum of the downsampled signals is given by Eq. $(4.77)$ in Oppenheim and Schafer's Discrete-time Signal Processing (3rd ed), which for downsampling factor $M=2$ ...


1

The answer to my question is: Essentials of Digital Signal Processing 1st Edition by B. P. Lathi https://www.amazon.com/gp/product/1107059321/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1 where in Section 6.6 you can find detailed discussions and good examples.


1

I haven't looked at the reference yet , but just to answer the question, yes filtering is performed prior to down sampling to avoid aliasing back in the out of band signals. However if your signal is already appropriately bandlimited you could forego the filter entirely. There's various reasons you might want to do other, unrelated, filtering after the ...


1

There are many advantages, but the most obvious to me Advantage 1 : Oversampling followed by decimation allows you use to simpler and smaller anti-aliasing filters. These filters cost less and take up less space on a PCboard. Advantage 2 : In multi-channels application, the tolerance and variation of the analog components of your anti-aliasing filters can ...


1

And additional consideration not mentioned that comes up in radio design is in the decision to use quadrature sampling of a baseband signal (as in "Zero-IF receivers") over a "Digital-IF" receiver that is achievable when the signal can be sampled at a much higher rate as a real signal. The Digital IF signal avoids the quadrature imbalance ...


1

With downsampling you have complete control over the process and it comes down to what compromise of processing complexity, delay, aliasing and loss of passband you can accept. With a lower rate A/D you are pretty much at the mercy of someone elses spectral trade-offs and in addition you get the quantization/noise of one analog pass. -k


1

Are the samples adhering to Nyquist (properly pre filtered)? If so, I would just resample to one common rate, prefereable >= max(rate1, rate2). And align them in time. Check out MATLABs resample() function. If the samples are not adhering to Nyquist, then you need to think about what they represent, how they are sampled and in what respect you need to ...


1

Here's how I like to think about the expression $$ \displaystyle \frac{1}{D} \sum_{k=0}^{D-1} e^{j 2 \pi k m / D}. $$ For any value of $D$, the first term is 1, and all of the terms lie on the unit circle. Assuming $D > 1$, each term after the first is found by rotating the previous term through an angle of $2 \pi m / D$ radians. If $m$ is not a multiple ...


1

You got the term $X \left( e^{j (\omega - 2 \pi)/2} \right)$ wrong. It is centered at $2\pi$ and it is non-zero in the interval $(2\pi-2\omega_0,2\pi+2\omega_0)$. So the results obtained in the frequency domain and in the time domain, respectively, are identical. Note that the term $X \left( e^{j \omega/2} \right)$ is $4\pi$-periodic, so the term $X \left( e^...


1

Sample rate conversation is easy in theory but tricky in practice. Assuming you want to convert to the standard rate of 44.1 kHz (not 44 kHz), you have an awkward conversion ratio. $3800 =2^3 \cdot 5^2 \cdot 19$ and $441 = 3^2 \cdot 7^2$ are mutually prime that means that rational sample rate conversion is impractical,so you need irrational sample rate ...


1

From that same page you link to: A signal is said to be oversampled by a factor of N if it is sampled at N times the Nyquist rate. So, you're sampling at $1\cdot10^4\,\text{Hz}$, that's $N=\frac{10^4}{140}\approx 71$; no need to subtract anything. Does this oversampling only reduce the noise introduced from the output of the analogue sensor (given ...


1

We can't tell you what your classifier does, sorry. But yes, you have a systematic bias in your data, and your classifier will cling to whatever is the strongest discriminator if it works as hoped. I will rename your classes to make this clearer: 100 audio samples : class 'Microphone 1 subclass 1' 100 audio samples : class 'Microphone 1 subclass 2' 100 ...


1

I want to downsample a finite section of an equidistant time-series by doing an FFT and dropping the upper part of the spectrum. Why? This one of the least efficient way to down sampling. See Why is it a bad idea to filter by zeroing out FFT bins? In order to down-sample you need to low pass filter first. There are many different ways of building a ...


1

You really need to look at the problem in the frequency domain. There are too many bit patterns that will create an obvious dilemma with respect to decimation, but these will invariably be in violation of the rules of the sampling theorem—something obvious in looking at the frequency spectrum, but perhaps not obvious looking at a list of sample values. For ...


1

Yes. With upsampling, the number of pixels increase. But it is not just an arbitrary addition of pixels. Generally, the idea is to end up with a higher resolution version of the original image. So certain algorithms may need to be used to interpolate, etc. With downsampling, on the other hand, the number of pixels decrease, and it would end up with a lower ...


1

Yes, that's correct. It's a natural extension of one dimensional up and down Sampling. However, one can define lattices (arbitary shapes) for sampling images, so one could downsample more in a particular axis than the other. Essentially instead of a sampling period, we have a sampling grid. There are benefits of using different freqeuency grids. Of course ...


1

Anytime you take away "actual" data samples away by donwsampling, yes, you are loosing on finer granular data in time domain and hence reducing resolution. However, consider, the following case, an input signal is first up sampled by 2(interpolation) and then down sampled by 2, does it decrease resolution of actual data, not quite, because the upsampled new ...


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