13 votes
Accepted

How do real-time convolution plugins process audio so quickly

Real-time low-latency partitioned convolution reverb with a long impulse response works by dividing the impulse response into unequally sized partitions. The shortest partitions (blocks) are at the ...
12 votes
Accepted

Number of DFT (FFT) Points Required for a Specific Frequency Resolution for an Oversampled Signal

The resolution in the DFT is given by: $ \frac{{F}_{s}}{N} $. Hence you need 10e6 / 100 = 100,000 samples to get the resolution you want. You may bring the signal to the baseband (demodulation) and ...
  • 42.6k
12 votes

What is the maximum possible frequency of human voice/speech(That can be generated through human vocal cords)?

The fundamental speaking frequency of humans can reach up to around 1kHz, although higher values than, say, 500Hz usually appear only while singing. The harmonics and non-tonal parts of speech can ...
  • 1,922
12 votes

What is the maximum possible frequency of human voice/speech(That can be generated through human vocal cords)?

Especially What is the maximum value of frequency that human speech can have? This depends on how exactly you define it. Fricatives ("s","f","sh" ...) and plosives (&...
  • 34.2k
10 votes
Accepted

Estimate the Filter Coefficients of 1D Filtration (Convolution)

This is a nice question. I will try solving it using 2 approaches (Which are basically the same). The solution is the Least Squares Solution: $$ \hat{h} = \arg \min_{h} \frac{1}{2} \left\| h \ast x - ...
  • 42.6k
9 votes

Doppler shift in time domain?

The term Doppler Shift is actually a bit of a misnomer. The frequencies are not actually shifted but they are scaled (see http://fourier.eng.hmc.edu/e101/lectures/handout3/node2.html for definition of ...
  • 34.2k
9 votes
Accepted

Adding Noise in Frequency Domain vs Time Domain

I usually like to add noise with my own code. Adding Whit Noise is really easy task given the signal as you have. All you need is to calculate your signal second moment at the frequency and add noise ...
  • 42.6k
9 votes
Accepted

Convolution Theorem using DCT

I did it for the DCT-I and DCT-II. At first I thought it is about circular convolution, but it is not. After desperate attempts to do it by myself I found the article: Convolution Using Discrete Sine ...
  • 356
8 votes
Accepted

Circular Convolution Matrix of $ {H}^{H} {H} $

If $ H $ is a matrix form of Circular Convolution then it is a Circulant Matrix. Being a Circulant Matrix means it can be diagonalized by the Fourier Matrix $ {F} $: $$ H = {F}^{H} D F $$ Where the ...
  • 42.6k
8 votes

Estimation of Amplitude, Frequency and Phase of Linear Combination of Harmonic Signal Beyond the Leakage Resolution of DFT

Solving the Linear Combination of Real Harmonic Signal The data model is given by: $$ x \left( t \right) = \sum_{i = 1}^{M} {a}_{i} \sin \left( 2 \pi {f}_{i} t + {\phi}_{i} \right) + n \left( t \right)...
  • 42.6k
7 votes
Accepted

Exercise Related to Frequency Resolution and SNR

Your calculation of the SNR is right and the DFT Bin Resolution is also OK. One thing you're missing is the effective resolution due to "Windowing" effect. The DFT of finite number of samples is ...
  • 42.6k
7 votes
Accepted

Why audio clipping produces harmonics?

Clipping is a non-linear operation. Consider a system that clips all input whose absolute value is larger than 1: $$ y(t) = \begin{cases}x(t)\text{ if }|x(t)|\leq 1 \\ 1 \text{ if } x(t) > 1 \\ -1 \...
  • 13.9k
7 votes
Accepted

Understanding the $\mathcal Z$-transform

Consider a liner discrete-time system. Assume we can define it in terms of an input-output relation as follows (you can assume a more general model but it is enough for our purpose): $$a_0y[n]+a_{1}y[...
  • 4,135
7 votes

Frequency Domain Filtering

This is just "faking" the magnitude response of an IIR filter. The output's magnitude spectrum looks just like it has been filtered by the IIR filter with the given frequency response. Although it may ...
  • 4,135
7 votes
Accepted

Computation of the Inverse DCT (IDCT) Using DCT Or IFFT

Have a look at Fast DCT Algorithm (PDF Version). It has both DCT and Inverse DCT using DFT (FFT). They show how to do a DCT and Inverse without the reflection trick. The standard (Less efficient ...
  • 42.6k
7 votes
Accepted

The Proper Way to Do Sinc Downsampling (DFT Downsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples

Interpolation in Frequency (DFT Domain) The implementation is well known. In MATLAB it will be something like: ...
  • 42.6k
6 votes
Accepted

How does the number of frequency-domain sampling points influence the outcome of an inverse FFT?

Regarding example 1: first of all, either the fft or the ifft needs to be normalised by the number of sampling points as you ...
  • 1,450
6 votes

Color Artifacts in Fourier Transformed Image

Some things you should keep in mind: Your image is real, keep your DFT Symmetric. Numerical issues might cause that after the Inverse DFT imaginary parts are lefts. Use either ...
  • 42.6k
6 votes

Impulse Response to Frequency Response in Octave

The Frequency Response of a system is the Fourier Transform of the Impulse Response of the system. Since we're in the real world and we have finite number of samples observed over finite time ...
  • 42.6k
6 votes

Understanding the frequency domain

In simple terms, Image shown here speaks for itself. Before speaking about Fourier Transform black magic lets understand idea behind it. Work of the Mathematician Joseph Fourier demonstrated any ...
  • 181
6 votes

FMCW Radar Signal Processing Flowchart / Ambiguity Function

The Ambiguity Function is just a name for 2D Correlator. It is known that given a shifted 1D Signal the optimal estimator for the shift (Range in RADAR / LIDAR, etc...) it the correlation with the ...
  • 42.6k
6 votes

How do I decide which frequencies are signal and which are noise?

There can't be. One man's signal is another man's noise. In fact, a communication system making the absolute most of a bandwidth would be spectrally white, just like white noise, and hence be ...
6 votes
Accepted

Idea for Noise Level Estimation / Automatic Thresholding in the Presence of Peaks

I'd do some small adjustments to your idea (You really nailed them). Assumptions The Signal Model - Signal + Additive White Gaussian Noise (AWGN) Probably we could generalize it more but this is ...
  • 42.6k
6 votes
Accepted

If a square wave is a sum of odd harmonic impulses, why is it continuous in the frequency domain?

As @Hilmar mentioned I think you get confused between Square wave and Rectangular function. In Wikipedia about Square Wave : A square wave is a non-sinusoidal periodic waveform in which the ...
6 votes
Accepted

What is the frequency representation of nonuniform sampling?

You might be interested in this particular reference paper: Digital Spectra Of Non-Uniformly Sampled Signals : Theories and Applications is a somewhat obscure reference (from 1988! can't go wrong!) ...
  • 1,080
5 votes

Number of DFT (FFT) Points Required for a Specific Frequency Resolution for an Oversampled Signal

The frequency resolution $f_\Delta$ is $$ f_\Delta = \frac{f_\mathrm{s}}{N}, $$ where $f_\mathrm{s}$ is the sampling frequency and $N$ is the FFT size. So $$ N = \frac{f_\mathrm{s}}{f_\Delta} = \frac{...
  • 4,061
5 votes

Oversampling and Aliasing

When upsampling, you don't really stretch the signal in time. You insert new samples between the existing ones, without modifying the times at which those samples were taken. One property of ...
  • 13.9k
5 votes

Why audio clipping produces harmonics?

assuming there were no harmonics (frequency components other than the fundamental that are at integer multiples of the fundamental frequency) in the first place, that means the input to the clipping ...
5 votes

Filter - Spatial Domain Versus Frequency Domain

It appears you need to study a bit on convolutional filtering of images, specifically on overlap add/ overlap save methods. From the links I can see your objective is to apply the filter defined in ...
  • 109
5 votes
Accepted

Frequency Domain Filtering

This sort of filtering is done all the time, but it doesn't have the effect you think it should. Suppose you have an IIR filter with an impulse response of $h[n]$ which is represented in the $z$ ...
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