13

Basics The amplitude of an IQ signal is just the vector magnitude, $\sqrt{I^2 + Q^2}$. The power of an IQ signal is the squared magnitude, $I^2 + Q^2$. When you see a logarithmic (dB) meter, it is usually measuring the log of the power, i.e. $10 \log_{10}(I^2 + Q^2)$. (This can also be calculated as $20 \log_{10}$ of the amplitude, but unless you already ...


7

An exponentially decaying envelope $a\exp(-b x)$ is a good choice, and is used for example in vintage Yamaha FM synthesizers. It has the favorable property that over any constant length time interval, by the end of the interval the envelope has decayed to a constant fraction of what it was at the beginning of the interval. Damped oscillation (with some ...


6

if the two audio signals are totally uncorrelated, the the squares of the two crossfade gains should add to 1. so, to prevent that dip, your crossfade function will look more like $\sqrt{\frac{1}{2}(1+t)}$ and $\sqrt{\frac{1}{2}(1-t)}$ rather than $\frac{1}{2}(1+t)$ and $\frac{1}{2}(1-t)$ for $-1 \le t \le +1$. note, for constant power crossfades, at the ...


5

Your code is bit unclear, especially generation of your signal. Python allows for vectorized operations so it is good to use it. What's more, it is good to clearly specify the sampling frequency of your signal and use it then. Also please remember to normalize your FFT by length of your signal (in this particular case) and multiply by 2 (half of spectrum is ...


5

The correct way to group multiple bins together is to multiply each complex fft bin output by its complex conjugate (which gives the bin power) then add all the bin powers together and divide by the number of bins in the group. If you want to display in db (which is the conventional approach) then take 10*log10() of the result. Negative db values are normal ...


5

That depends to a very large degree on the type & sensitivity on the headset, the gain of the amplifier and the frequency. I don't think there is a reasonable rule of thumb, this will be all over the place.


5

Without an artificial ear and calibrated SPL meter your not going to obtain a valid measurement (even then the SPL will vary per earphone fitting). With earphones and a multimeter, you can only really ballpark the measurement e.g. output a full scale tone, and measure the voltage at the terminals (should be OK to do this by parallel output of the playback ...


5

Both amplitude and frequency modulated radio signals nowadays use quadrature modulation and demodulation as a mean to transfer and receive radio signals. This question is ill-defined – a signal doesn't use quadrature modulation/demodulation, transmitters/receivers do. So, your question is, if we try to "rescue" it, is Do modern FM receivers/...


4

Suppose that we have a continuous-time periodic signal $\displaystyle s(t) = a_0 + \sum_{n=1}^N a_n \cos(n\omega_0 t + \theta_n)$. What does this mean? Do we have a trace of $s(t)$ on some recorder chart and the trace looks periodic? If we did, the question to be solved would be trivial since we could simply measure the maximum and minimum values of $s(t)$...


4

Generally, the frequency estimation problem decouples from the amplitude + phase estimation problem. As I said in the comments, you could just do: $$ \hat{A} = \left|\sum_{n=0}^{N-1} x_n e^{-j 2\pi\hat{f} n} \right| $$ where $\hat{f}$ is your frequency estimate. Regarding your issues: because the number of points isn't high enough to hit the right ...


4

The usual way to estimate the amplitude of a particular frequency is to use the Goertzel algorithm. There is a good write-up by Rick Lyons here. Even though Rick's writeup is about single tone detection, it can be applied when multiple tones are present, too.


4

Not really, as the transform is real. However, one could interpret the sign as a poor man's phase, being "quantized" or restricted to values $0$ or $\pi$. In other words, $1 = 1.e^{0.\imath}$ and $-1 = 1.e^{\pi.\imath}$. [EDIT] There are some instances where people use the sign of DCT or (real) wavelet coefficients, for subpixel image registration or ...


4

A DCT is equivalent to a DFT of real data that is doubled and mirrored, thus rendering it symmetric. The DFT of any symmetric real signal has a phase of zero (its all cosines, no antisymmetric sine components).


3

In $2^{2n}$-QAM with a square constellation, there are $4$ "corner" points and $4(2^n-2)$ "edge" points, and $(2^n-2)^2$ "interior" points. The conditional symbol error probabilities given that each type of point is transmitted, are $$\begin{align} P_e(\text{corner}) &= 2Q(x) - Q^2(x)\\ P_e(\text{edge}) &= 3Q(x) - 2Q^2(x)\\ P_e(\text{interior}) &...


3

Maybe you have a look at Goertzels Algorithm.


3

As people in the other answer have been asking for a code snippet (and as I don't have enough reputation to comment on answers), here's the other answer implemented in C# (which should be easy enough to convert to other languages) /* returns a float array with two indexes representing the volumes of the left (index 0) and right (index 1) channels when t is -...


3

The antenna does not do Fourier analysis and has no idea that there is a carrier signal and an upper sideband and lower sideband. Whatever the signal applied to the antenna via electrical wiring or coax cable or transmission line, the flow of current in the antenna causes an electromagnetic wave (coupled time-varying electrical and magnetic fields) to be ...


3

Try adding a gain of 16 before your low pass filter, or equivalently using a low pass filter with a passband gain of 16 instead of 1.


3

That's correct, $0.4053$ is the approximate magnitude of the frequency response of linear interpolation at the Nyquist frequency. With the definition: $$\operatorname{sinc}(x) = \frac{\sin(\pi x)}{\pi x}$$ the exact value is: $$\operatorname{sinc}^2\left(\frac{1}{2}\right)= \left(\frac{\sin\left(\frac{\pi}{2}\right)}{\frac{\pi}{2}}\right)^2 = \left(\frac{...


3

There is no issue of frequency resolution in a typical modulation and demodulation scheme. (unless you want to implement some frequency/signal detectors) Putting two message signals in adjacent channels requires that their spectrums do not overlap. In your case you should be able to specify the associated bandwidths of those two slowly changing analogue ...


3

To extract only the carrier with a band-pass filter, the filter pass-band has to be narrower than the modulating frequencies, or else some of the envelope modulation will "leak" through the filter. Also note that a very narrow filter has a long settling time, so you will need a long enough test signal.


3

To a first approximation, a plucked string has an exponential decay, so your envelope will look like $$x(t) = a \exp -bt.$$ The physical explanation for this is simple: when you pluck the string, you put a certain amount of energy into the system. Over time, energy is lost. At any given time, the amount of energy lost is proportional to the amount of energy ...


2

Consider your carrier signal as $E_c\cos W_{ct}$ and your message signal is $E_m \cos W_{mt}$. The double side band plus carrier signal is, $ E_c\cos(W_{ct})+(E_c\cos(W_{ct})E_m\cos(W_{mt})) $ $ E_c\cos(W_{ct})+\frac{1}{2}(E_cE_m[\cos(W_{ct}+W_{mt})+\cos(W_{ct}-W_{mt})]) $ $ Ec*Cos(W_{ct})+\frac{1}{2}E_cE_m\cos(W_{ct}+W_{mt})+\frac{1}{2}*Ec*Em*Cos(W_{ct}...


2

For periodic signals, the maximum peak-to-peak amplitude is dependent in the relative phase of each harmonic, as well as their magnitudes. Do you have that information? If so, you can numerically evaluate all the local maxima and minima and sort.


2

This is a continuation of the (music-dsp) thread started by Element Green titled: "Algorithms for finding seamless loops in audio" As far as I know, it is not published anywhere, although I have recently been informed that a similarly-themed paper by Marco Fink, Martin Holters, and Udo Zölzer has been presented at the 2016 DAFx conference, which is a while ...


2

Many audio FFT visualizations use log(magnitude) instead of linear, as that makes it easier to find a scale that makes data visible a graph. The energy contained in band that contains multiple FFT result bins would be the sum, not the max. If the "certain amount" of samples you grab for each FFT is a small fraction of those per 1/24 second, then you may ...


2

There are a number of ways to do this, but I like this way: // very rough pseudocode step_size = 9000000 / width_of_window; // 9000000 or however many points for each pixel in width of window figure out what portion of the audio stream this x value corresponds to take step_size shorts corresponding to position in audio stream find the minimum and ...


2

I did a fair amount of frequency-content visualization in the past, although I don't have the code in front of me... Sorry I don't have more time but I think this might be of help, so here's what I recall: First off, I'm not sure if this is part of what is giving you headaches, but since a real signal run through an FFT doesn't have a complex (phase) signal ...


2

Fourier transforms and differentiation are indeed very different, but your intuition is still not entirely wrong. Here's how to make sense of it. Let's assume you have a signal that is essentially sine-shaped locally, i.e. we can write it as $s(t) = a \sin(2 \pi f t)$ for a times $t$ close to some time $t_0$. In other words: The signal oscillates like a ...


2

A few reasons why this is a terrible idea: Unless your frequency is an exact multiple of the FFT window size, it'll be spread over adjacent FFT bins. You're mentioning Morse code, so your carrier is modulated. This is not a constant tone, it has a changing envelope, and thus, its spectrum is convolved by the spectrum of the envelope. As a result, you won't ...


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