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11

To be able to analyze what a low pass filter does first you would need to understand what a Fourier transform is, hence some theory first. The Fourier transform essentially represents the time-domain information stored in some function (a square wave in your case) in terms of frequencies. A simple example would be a sine wave $sin(2\pi f_{c} t)$ which ...


7

The baseband QAM signal is complex, and the only way to draw it is by doing two drawings, one for the in-phase (real) component, and one for the quadrature (imaginary) component. The passband QAM signal, though, is real, and it is a pulse-shaped carrier whose amplitude and phase depend on each symbol. Myself, I would "draw" it using Matlab or some other ...


6

The hydrophone has -180 dB 1V/uPa or -60 dB V/Pa. 1 Pa produces hence 1mV or, other way around, the sensitivity is 1mV/Pa. Peak voltage is 5.64 peak to peak. That's 2.82V peak or 2V RMS. A full scale sine wave has 2 V RMS which is 2000 Pa. dBSPL is referenced against 20uPa so 2000 Pa is equivalent to 160 dBSPL. The clipping point of your wave file ...


6

In principle you can, in practice you almost can. The square wave consits of sinusoids with frequencies that are at multiples of the fundamental one (the inverse of the length of one high and one low). These are called harmonics, as you already seem to know. The low pass filter can remove all frequencies above the fundamental one, and you are left with only ...


6

If your signal is really as simple as $$x(t)=A\sin(\omega_0t)\tag{1}$$ with known $\omega_0$, and you have observations $y(t_i)$, which are noisy samples of $x(t)$ at known time instances $t_i$, then a simple solution would be the least squares estimate $$\hat{A}=\frac{\displaystyle\sum_iy(t_i)\sin(\omega_0t_i)}{\displaystyle\sum_i\sin^2(\omega_0t_i)}\tag{2}$...


5

Depends on assumptions you are willing to make and what type of signals are you trying to sample, but in theory I think that sampling rate equal to the Planck time would be a gold standard for anything... This translates to sampling frequency of $1.855 \times 10 ^ {43} \mathtt{Hz}$ ($18.55$ tredecillion hertz). Personally I believe that machines will never ...


5

First of all, welcome to DSP SE. What you see in the image you have linked is termed (spectral) leakage. When you are dealing with the Fourier series you deal with a periodic continuous function which is "decomposed" into a (possibly) infinite sum (series). Then, when you go to the Fourier transform, you have a non-periodic function (which you ...


5

A big question. Plz have a look at this first https://en.wikipedia.org/wiki/Sound_recording_and_reproduction. Sound is highly related to vibration. Sound is generated by vibration of a sound source, and you can hear a sound is because of the vibration of eardrum. Sound Recording Sound pressure is the local pressure deviation from the ambient (average or ...


4

I think you posted similar question 3 days ago, regarding your teacher claiming that $\sin 2x$ is not a sinusoidal function. Nevertheless this function is definitely sinusoidal. Otherwise how come we can say that signals can be decomposed into sums of sinusoids (and cosinusoids)? You have plenty of orthogonal waves: $\sin x, \ \sin 2x, \ \sin 3x, \ldots$, ...


4

I'd like to point out Heisenberg Uncertainty principle, based on which theoretical achievable precision is limited. It states that one can not measure two complementary qualities (e.t. here time and charge) concurrently and there is a trade off between amount of precision you can get from one or another. In ADCs, for example theoretical limit for resolution ...


4

When using a constant tone audio beacon, beware of room echoes causing multi-path interference and distortion, especially around the leading and trailing portions of your received waveforms. Try using a frequency sweep instead of a constant tone for your transmit waveform. This might provide you with a sharper correlation peak that is less likely to have ...


4

The fundamental property of averaging filters (in swear words, a linear system) is that the output of a sine is a sine of the same frequency, albeit of zero amplitude. So: Which non-trivial moving average weights would you need to find to get a filter that returns the same output as its input? An averaging in phase with the sine: take a filter full of ...


4

Zero-order hold will result in a piecewise-constant waveform. Linear interpolation will result in a piecewise-linear waveform. If you want a piecewise-quadratic or piecewise-cubic or higher order polynomial interpolation, it will not appear much different from the original bandlimited waveform.


3

Neither of these tones is an exact number of samples at 48 kHz, but you can calculate the periods as follows: $\frac{48000}{441} = 108.84$ samples $\frac{48000}{700} = 68.57$ samples


3

No, and the reason is not so much a question of how fast one can sample a continuous-time signal (as the accepted answer and another one says) but rather the impossibility of representing a real number with perfect accuracy via a quantized representation of the real number (as noted in the answer by Marcus Muller). At best, even if we assume an infinite ...


3

Is it theoretically possible to perfectly quantize a continuous signal? No. A quantization has an information content obviously countable as bits. Now, if you have a continuously distributed 1D random variable $X$, then the event that any of these real numbers $x$ occurred is unbounded ("infinite"): $$I(x) = -\log_2\left(P(X=x)\right)$$ So, for ...


3

Please note that you cannot implement a band-limited oscillator with a pure (stateless) function like: Sample s = saw(x); The reason is that the function must be aware of the rate at which x change to generate a signal with the correct bandwidth For example, let us assume your sample rate is 48kHz. If you call your function in this order: saw(0.00000000);...


3

The AM or medium wave band extends from 526.5 kHz to 1606.5 kHz in Europe or 535 kHz to 1705 kHz in the US. Ultrasound (not supersound! :-) frequencies range from 20kHz and up: However, a bigger problem is that AM stations broadcast using electromagnetic radiation, whereas sound travels by acoustic waves in the air.


3

This is a question where theory and practice will diverge somewhat. Theory I assume that by "frequencies" you mean sinusoids of varying frequency. In that case, yes, you're correct, for any amplitudes $a_1$ and $a_2$ and frequencies $f_1$ and $f_2$ (where $f_1 \ne f_2$), the signals $$ x_1(t) = a_1e^{j2\pi f_1 t} \\ x_2(t) = a_2e^{j2\pi f_2 t} $$ are ...


3

Piano tones are actually quite complicated. The initial strike is full of non-harmonic tones that quickly dampen down. After that, the harmonics vary from note to note, piano to piano. I suggest you look at some actual sample files, capture a whole number of somewhat consistent waveforms, do a DFT, and read the coefficients from there. As for the other ...


3

The best wave form function I found so far is in this video. In terms of my experience this is the formula: Y = sin(2 * pi * frequency * time) * exp(-0.0004 * 2 * pi * frequency * time) Adding overtones: Y += sin(2 * 2 * pi * frequency * time) * exp(-0.0004 * 2 * pi * frequency * time) / 2 Y += sin(3 * 2 * pi * frequency * time) * exp(-0.0004 * 2 * pi * ...


3

Natalia Molinero Mingorance, Welcome to the DSP community. What you have is basically a shifted periodic signal. Why? Because what you have is equivalent (Given many samples) of having a periodic signal which you started sampling at $ 0 $ and then we shit it to the real place you started sampling it. Yea, there is the edge case, since it might not have ...


3

Does radio communication have to account for the doppler effect? Yes. Would be pretty terrible if that wasn't the case: RADAR wouldn't work! Do moving objects such as planes and rockets have to account for this, Yes. Phones in cars and trains, too. Your 5G NR phone of the future operating above 60 GHz, will have to do that at walking speeds, too. or is ...


3

Build a basis set with your frequency and match your signal. It is straightforward linear algebra: $C$ is portion of cosine $S$ is portion of the sine $U$ is a vector of ones (DC) $$ X = a C + b S + c U $$ $$ X \cdot C = a (C \cdot C) + b (S \cdot C) + c (U \cdot C) $$ $$ X \cdot S = a (C \cdot S) + b (S \cdot S) + c (U \cdot S) $$ $$ X \cdot U = a (C \cdot ...


3

Sound is a compression wave in a fluid media. In other words: sound is air molecules wiggling back and forth. No air = no sound. Sound is generated if something vibrates and jostles the air molecules. For example: if you hit a drum head, the head gets displaced and wiggles back and forth for a bit. This in turn wiggles the air around it. The moving air ...


2

The energy in the ticks is distributed to higher frequencies, too. The base frequency probably is not very strong. You might be looking for broadband signals. I would try to take a time difference of amplitudes. Ticks will have steep temporal edges.


2

Since you are looking for a low frequency periodicity in the amplitude envelope of your sound clip, and not the tone waveform or pitch, you might try squaring or taking the absolute value of your signal before applying the fft, and then ignoring higher frequency bins in the result (similar to a cheap AM demodulator).


2

Well to clear your doubt ,i would like you to ask you a question. What would be the value of angular frequency × Time period = ?? Okay,so in eq - $\omega \times t$ . if we put $T$ in place place of $t$, given that the wave is sinusoidal, the value to that eq would be $2\pi$. By definition $T$ is the time taken to complete one oscillation so when we ...


2

You could create a standard 2 channel wav file. 1 channel for the real part and 1 for the imag. Wav files supports both 16bit integer, 32bit integer and 32bit floats etc. The channel data will be interleaved (I believed it's called). Meaning that your data will be written: [REAL][IMAG][REAL][IMAGE]... Prolly just like your own bin file. Standard programs ...


2

The quality you are looking for is called "Timbre". When each instrument plays a note it generates not only the fundamental frequency but a series of harmonics or overtones. The relationship in amplitude of all the overtones creates the instrument's tonal colour. So if a trumpet plays a C note it will generate the fundamental C, as well as a specific set of ...


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