What will be the Shannon equation for a noiseless signal?
Means if noise will be 0 then what will be the value of signal to noise ratio(S/N)?
SNR would be infinity and you would have theoretical infinite transmission rate. But you always have noise, you know.
Related
I'm creating a procedural engine sound generator heavily inspired by AngeTheGreat's engine simulator, but using some trigonometry functions to calculate the piston and crankshaft movement instead of rigidbodies.
I'm starting with the most basic piston movement sound generation, by taking some educated guesses (I have zero experience with audio signal processing) I assumed I could generate the audio signal by using the piston velocity, which is calculated as derivative of piston position ((piston_position - previous_piston_position) / dt), the piston position is modulated by a bit of noise, to simulate the piston sliding along the cylinder walls.
So far so good, it seens to have a expected result, considering I haven't added any kind of audio processing steps, it's really simple and sounds like a piston movement. But it gets really loud as the engine speed increases, here is a demonstration of a simple v2 engine, I reduced the output signal to 10%, to avoid hearing damage. As you can see in the video, in the soundwave representation in the bottom-left, the signal goes beyond the [-1, 1] range.
So some question about piston movement audio signal generation:
Is velocity input a good way to generate the piston movement audio signal?
Is amplitude of the sound related by the piston frequency in real life? Shouldn't it have a constant amplitude, but with higher frequency?
How I tweak the signal generation to have less amplitude at higher rpms? I should take sound propagation speed in the air into consideration?
I've tried using the piston position itself, but it sounds way more like a sine wave, the value oscilates between [0, top position] range, not [-1, 1] range, and it generates a constant non-zero signal when the piston isn't moving.
Another way to think of my problem: If I wanted to simulate the audio signal coming from a oscilating speaker, how I would generate the audio signal, taking into consideration only the speaker position? I would need to use the speaker velocity too?
I am doing filter convolution by using fft (FFTW). I experience something I can not understand.
I have an input x(n) which I want to apply a filter IR u(n). Both length N. So I zero pad both e.g. to 2n and do FFT of both to get X(n) and U(n). if I just do X(n)*U(n) and IFFT I get a signal y(t). If I listen to the signal there is no sizzling, all sounds ok. For speeding up the programm and saving memory I tried to take advantage of symmetrie of U(n) and X(n)and to use only first half of U(n) and X(n) and zero padding the second half. So I did X(n0...n/2,0,0,0,0,..,N)U(n0,..,n/2,0,0,0,..,N) and IFFT.
The resulting output sounds not different to the result when multipling full length XU but there is strange subtile sizzling noise audible laying on the output. Mostley apparent on loud/resonant input signal parts, sounds almost like clipping the stage. I did not change anything in the scaling in both methods so, I don´t understand whats going on. Could someone help me out with an idea?
Is it wrong to just use half of U and X and zero pad the rest , must I use the full length? Or does this change e.g. scaling?
You can not simply set part of your signal spectra to zero. Any real signal (with no imaginary component) has a conjugate complex spectrum. I guess this is the symmetry you are talking about. If you set part of the spectrum to zero your signal in the time domain will be complex and completely different from the original signal you started with.
If you want to speed up your computation reduce the number of your samples you are working with
I want to do precise guitar tuner, this is usually done by many via computing FFT and getting peak. But this is of low appliance for several reasons:
Discrete precision, gives insuffient resolution for tuning bass guitar.
High computation time and complexity, when trying to increase buffer size(and/or sampling rate). Introduces visible delay(lag).
Most of frequency range where concentrates all FFT's precision is unused. Everything above 1-2 khz is not appliable for tuning musical instruments.
There should be simplier way for signals that have single-frequency sinusoidal shape. Given small enough buffer (say it 256 samples with 96khz sampling rate) - how could you measure a base(lowese) frequency?
In simple words: How to find frequency F, so that difference of "sine signal of frequency F" and "actually recorded signal" would give minimal error, than for any frequency, other than F ? (so we can definetely conclude that sinusoid of frequency F is best approximation of recorded sound buffer).
PS. Anything, but not using FFT!
Here is a simple approach based on zero crossing. It relies on being able to map the instrument signal to a simple sinuoid. This may work OK when signal to noise ratio is high, but is not a very robust method.
Bandpass filter around the fundamental frequency of the tone you want to tune for. Example 82.41 Hz for low E string on guitar.
Consider a window of the last N samples. Set it to ex 100ms to update the pitch estimate 10 times per second.
Perform zero-crossing detection with a threshold value T. T could be set to 10% of signal peak for example. Count the periods between each zero crossing, collect them in an array.
Take the median of the periods to get your pitch estimate
You can also compute the quantiles of the periods to estimate how reliable the method is. If they give very different numbers from the median, then the method is not working well.
The approach can be extended by computing autocorrelation on the zero-crossings, as described in
https://www.cycfi.com/2018/03/fast-and-efficient-pitch-detection-bitstream-autocorrelation/
I'm trying to get a qualitative handle on the amount of static or noise present in a audio stream. The normal content of the stream is voice or music.
I've been experiementing with taking the stddev of the samples, and that does give me some handle on the presence of voice vs. empty channel noise (ie. a high stddev usually indicates voice or music)
Was wondering if anyone else had some pointers on this.
Doesn't the peak value give you the answer? If you're looking at a signal from a good ADC, the ambient level should be in the 1's or 10's of counts, while voice or music will get up into the thousands of counts. Is there some kind of automatic gain control that makes this strategy not work?
If you need something more complex, the peak to RMS ratio might be a bit more reliable than simply RMS level (RMS = stddev). Pure noise will have a ratio of around 3-5, while sinusoids, for instance, have a peak to RMS ratio of 1.4. However, you can get more discrimination by looking at the spectrum of the signal. Static is usually spectrally smooth or even flat, while voice and music are spectrally structured. So a Fourier transform might be what you're looking for. Assuming a signal x that contains, say 0.5 seconds worth of data, here's some Matlab code:
Sx = fft(x .* hann(length(x), 'periodic'))
The HANN function applies a Hann window to reduce spectral leakage, while the FFT function quickly calculates the Fourier transform. Now you have a couple of choices. If you want to determine whether the signal x consists of static or voice/music, take the peak to RMS ratio of the spectrum:
pk2rms = max(abs(Sx))/sqrt(sum(abs(Sx).^2)/length(Sx))
I'd expect pure static to have a peak to RMS ratio around 3-5 (again), while voice/music would be at least an order of magnitude higher. This takes advantage of the fact that pure white noise has the same "structure" in time and frequency domains.
If you want to get a numerical estimate of the noise level, you can calculate the power in Sx over time, using an average:
Gxx = ((k-1)*Gxx + Sx.*conj(Sx))/k
Over time, the peaks in Gxx should come and go, but you should see a constant minimum value corresponding to the noise floor. In general, audio spectra are easier to look at on a dB (log vertical) scale.
Some notes:
1. I picked 0.5 seconds for the length of x, but I'm not sure what an optimal value here is. If you pick a value that's too short, x will not have much structure. In that case, the DC component of the signal will have a lot of energy. I expect you can still use the peak to RMS discriminator, though, if you first toss out the bin in Sx corresponding to DC.
2. I'm not sure what a good value for k is, but that equation corresponds to exponential averaging. You can probably experiment with k to figure out an optimal value. This might work best with a short x.
There are different kinds of noise. White, pink, brown. Noise can come from many places. Is a 60hertz hum noise or signal?
For white noise, I'd look at the fft and find the lowest value to see what your noise floor is.
Without any user interaction, how would a program identify what type of waveform is present in a recording from an ADC?
For the sake of this question: triangle, square, sine, half-sine, or sawtooth waves of constant frequency. Level and frequency are arbitrary, and they will have noise, small amounts of distortion, and other imperfections.
I'll propose a few (naive) ideas, too, and you can vote them up or down.
You definitely want to start by taking an autocorrelation to find the fundamental.
With that, take one period (approximately) of the waveform.
Now take a DFT of that signal, and immediately compensate for the phase shift of the first bin (the first bin being the fundamental, your task will be simpler if all phases are relative).
Now normalise all the bins so that the fundamental has unity gain.
Now compare and contrast the rest of the bins (representing the harmonics) against a set of pre-stored waveshapes that you're interested in testing for. Accept the closest, and reject overall if it fails to meet some threshold for accuracy determined by measurements of the noisefloor.
Do an FFT, find the odd and even harmonic peaks, and compare the rate at which they decrease to a library of common waveform.. peak... ratios.
Perform an autocorrelation to find the fundamental frequency, measure the RMS level, find the first zero-crossing, and then try subtracting common waveforms at that frequency, phase, and level. Whichever cancels out the best (and more than some threshold) wins.
This answer presumes no noise and that this is a simple academic exercise.
In the time domain, take the sample by sample difference of the waveform. Histogram the results. If the distribution has a sharply defined peak (mode) at zero, it is a square wave. If the distribution has a sharply defined peak at a positive value, it is a sawtooth. If the distribution has two sharply defined peaks, one negative and one positive,it is a triangle. If the distribution is broad and is peaked at either side, it is a sine wave.
arm yourself with more information...
I am assuming that you already know that a theoretically perfect sine wave has no harmonic partials (ie only a fundamental)... but since you are going through an ADC you can throw the idea of a theoretically perfect sine wave out the window... you have to fight against aliasing and determining what are "real" partials and what are artifacts... good luck.
the following information comes from this link about csound.
(*) A sawtooth wave contains (theoretically) an infinite number of harmonic partials, each in the ratio of the reciprocal of the partial number. Thus, the fundamental (1) has an amplitude of 1, the second partial 1/2, the third 1/3, and the nth 1/n.
(**) A square wave contains (theoretically) an infinite number of harmonic partials, but only odd-numbered harmonics (1,3,5,7,...) The amplitudes are in the ratio of the reciprocal of the partial number, just as sawtooth waves. Thus, the fundamental (1) has an amplitude of 1, the third partial 1/3, the fifth 1/5, and the nth 1/n.
I think that all of these answers so far are quite bad (including my own previous...)
after having thought the problem through a bit more I would suggest the following:
1) take a 1 second sample of the input signal (doesn't need to be so big, but it simplifies a few things)
2) over the entire second, count the zero-crossings. at this point you have the cps (cycles per second) and know the frequency of the oscillator. (in case that's something you wanted to know)
3) now take a smaller segment of the sample to work with: take precisely 7 zero-crossings worth. (so your work buffer should now, if visualized, look like one of the graphical representations you posted with the original question.) use this small work buffer to perform the following tests. (normalizing the work buffer at this point could make life easier)
4) test for square-wave: zero crossings for a square wave are always very large differences, look for a large signal delta followed by little to no movement until the next zero crossing.
5) test for saw-wave: similar to square-wave, but a large signal delta will be followed by a linear constant signal delta.
6) test for triangle-wave: linear constant (small) signal deltas. find the peaks, divide by the distance between them and calculate what the triangle wave should look like (ideally) now test the actual signal for deviance. set a deviance tolerance threshold and you can determine whether you are looking at a triangle or a sine (or something parabolic).
First find the base frequency and the phase. You can do that with FFT. Normalize the sample. Then subtract each sample with the sample of the waveform you want to test (same frequency and same phase). Square the result add it all up and divide it by the number of samples. The smallest number is the waveform you seek.