Skip to main content
Share Your Experience: Take the 2024 Developer Survey
17 votes
Accepted

Why is the convolution of two sine waves a sinc function?

You are not convolving two sine waves, you are convolving two short snippets of sine waves. A snippet of a sine wave is the same as a real (infinite) sine wave multiplied with a rectangular window. ...
Hilmar's user avatar
  • 45.3k
13 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 (&...
Hilmar's user avatar
  • 45.3k
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 ...
Max's user avatar
  • 2,368
10 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 ...
dogtype's user avatar
  • 366
10 votes
Accepted

Why do we calculate the second half of frequencies in DFT?

First, there's some pedantics to get out of the way: it's not FFT or DFT -- the FFT is just a specific method of computing the DFT that's advantageous under many circumstances. Any DFT takes $N$ ...
TimWescott's user avatar
  • 12.8k
9 votes
Accepted

Why does interpolation with zeros introduce frequency artifacts?

First of all, you should (re-)read the corresponding chapter(s) in your textbook or lecture notes. Understanding these basic properties of discrete-time signals is essential. Second, what you see is ...
Matt L.'s user avatar
  • 90.3k
8 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 ...
msm's user avatar
  • 4,295
8 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!) ...
Jdip's user avatar
  • 6,265
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[...
msm's user avatar
  • 4,295
7 votes
Accepted

Why does the frequency in the DFT have to be an integer?

There are a few different ways to interpret the math of the DFT. The one I find most suitable to explain this and other properties of the DFT assumes that the continuous Fourier domain was sampled, ...
Cris Luengo's user avatar
  • 2,584
7 votes

S domain vs frequency domain?

The s domain is synonymous with the "complex frequency domain", where time domain functions are transformed into a complex surface (over the s-plane where it converges, the "Region of ...
Dan Boschen's user avatar
  • 51.9k
6 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 $z$ ...
Peter K.'s user avatar
  • 25.8k
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 ...
rahulb's user avatar
  • 181
6 votes

Definition of the DFT / FFT Bin Size

Let's assume we have a sample rate of $f_s=10 kHz$ and FFT size of $N=1000$ Your bin spacing is $\delta f = 10 Hz$. It's simply the sample rate divided by the FFT size. That's all there is to it. ...
Hilmar's user avatar
  • 45.3k
6 votes
Accepted

Definition of the DFT / FFT Bin Size

I don't think Hilmar's answer is very good as it interprets the DFT within a specific application context. That confuses issues. The DFT is a tranform that works on a set of N samples. The samples ...
Cedron Dawg's user avatar
  • 7,560
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 ...
Marcus Müller's user avatar
6 votes
Accepted

How do I perform a time domain phase shift in the frequency domain?

Let’s be clear on what we will refer to as time delay and phase shift. Due to the common association of individual frequencies as sinusoids many confuse delay and phase shift as being equivalent. ...
Dan Boschen's user avatar
  • 51.9k
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 ...
m-sh-shokouhi's user avatar
6 votes
Accepted

When if an FFT more efficient than Goertzel?

If you implement the Goertzel algorithm P times to detect P different spectral samples, Goertzel is more efficient (fewer multiplies) than the N-point FFT when P < log2(N).
Richard Lyons's user avatar
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 ...
PSK's user avatar
  • 109
5 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 - ...
Royi's user avatar
  • 19.7k
5 votes
Accepted

Discontinuities in the FFT

Your parameters aren't correct for producing a whole number of cycles for each component. For each $i$ the value of $ \frac{\omega_{i}}{\omega_{s}} N $ has to be a multiple of $ 2 \pi $. Hope this ...
Cedron Dawg's user avatar
  • 7,560
5 votes
Accepted

Why do frequencies of analog signals range from $-\infty$ to $\infty$ while frequencies of digital signals are restricted to $[0,2\pi]$?

The digital frequency span of 0 to $2\pi$ is the normalized angular frequency given in units of radians per sample. For example, if we had a frequency tone that went $0.2\pi$ radians/sample, then it ...
Dan Boschen's user avatar
  • 51.9k
5 votes
Accepted

Absolute value based AM envelope detection viewed in the frequency domain

$\DeclareMathOperator{\sgn}{sgn}$ The modulating signal in AM is $$s(t) = C + a(t)\text,$$ where $a(t)$ is the (audio) amplitude, and $C$ is a constant so that $s(t) \ge 0 \;\forall t$. (Otherwise, ...
Marcus Müller's user avatar
5 votes

What is the Effect of Multiplying a Function by the Unit Impulse Function in the Frequency Domain?

I think there is a slight typo in Robert Bristow-Johnson's answer. Should be \begin{align} x(t) &= \frac{1}{2 \pi} \int\limits_{-\infty}^{\infty} X(\omega) e^{j \omega t} \, \mathrm{d}\omega\\ \\ ...
Marko Kosunen's user avatar
5 votes

Proof of fourier transformation of multiplication of two signals

I am very thankful to Dilip-sarwate and Gilles, who took their precious time to understand my problem and guide me. So, Now I'm going to write the correct solution to my question. Which is as follows: ...
Gurpreet Singh's user avatar
5 votes

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

A square wave is not a Sinc function in the frequency domain, but a sampled Sinc function (Even as a continuous function, the non-zero values are samples of the Sinc function in frequency). An ...
Dan Boschen's user avatar
  • 51.9k
5 votes

Relation of zero-padding and frequency resolution

why do I get "better" frequency resolution in case of adding zero-padding to this signal. You do and you don't. Zero padding increases resolution by interpolating between existing data ...
Hilmar's user avatar
  • 45.3k
4 votes
Accepted

What's the meaning of a complex zero/pole?

We usually talk of $j\omega$ when we're also interested in the Laplace transform of a signal / system, but want to just talk about the frequency response. The physical meaning of the imaginary part ...
Peter K.'s user avatar
  • 25.8k

Only top scored, non community-wiki answers of a minimum length are eligible