Questions tagged [dft]

The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in a (primal) domain (time, space) and the dual frequency domain. DFT requires an input sequence which is discrete, such as a sampling from an analogue audio signal.

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135 views

On-Chip DFT Engine vs Software DFT

I'm new to signal processing. I'm trying to build a network analyzer. So far I was only considering getting the output signal through a 16-bit ADC and then do its corresponding windowing and DFT to ...
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2k views

DFT of a unit step

Studying DSP on my own. Intuitively I understand that DFT of unit step is $\delta[n]$ , but I can't demonstrate it mathematically. Here is what I have so far $$ DFT\{u[n]\} = X_k = <\textbf w^{(k)...
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65 views

creating this famous basic nyquist theory photo

Hello i ha built this code which create a only one replica of the data, how can i create the whole photo shown bellow of many cycles as shown bellow? i read in the internet that zero padding could ...
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Quite confused with Fourier Analysis results

So I'm meant to show how the DFT can find the frequencies, and respective amplitudes, associated to some data. And I have this data set from the curve $$ f(t) = 1 + 2\cos(2\pi t) + 4\cos(4\pi t) $$ ...
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90 views

Factor unknown for cosine filter DFT

To calculate the DFT of the fundamental frequency of a discrete signal, Why multiply by $\frac 2N$ in the equation below? Where does that factor come from? \begin{align} C_{k_n} &= e^{-j\left(\...
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73 views

Calculating phase only component of a signal in MATLAB

I am working in the field of digital signal processing. Recently I read a paper that tells about phase only component of a Signal. It is given that the phase only component is calculated as $r_{phase}=...
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1answer
88 views

Trouble understanding discrete Fourier Transform

In the paper Calculation of a constant Q spectral transform - J.C.Brown it is mentioned The conventional linear frequency representation given by the discrete Fourier transform gives rise to a ...
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1answer
211 views

Use of FFT to compute frequency response [duplicate]

Is there an algo that uses fft to compute the frequency response of an FIR? Currently I follow the textbook method of evaluating the $z$ transform at $e^{-j\omega}$ for $\omega$ running from $0$ to $\...
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192 views

what is the preffered data and FFT length for blackman harris window for improving Accuracy due to ENBW Consideration of window?

for Rectangular window if data length is 1K then FFT Length Should be 1K FFT only because ENBW of rectangualr window is 1.0 but for Minimum 4-Sanple BlackmannHarris window is 2.0. so for improving ...
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1answer
674 views

how to sample sine wave to 4 points dft output

sinusoid x(t)=1+sin(2*pi *500) sampling rate :1000 samples/s Can I have 4 points DFT output with the above data.
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215 views

What Are the Suggested Resources for Extensive Knowledge About the Fourier Transform (DFT, FFT, etc…)? [closed]

I would like to improve my knowledge about Fourier Transform related subjects. What are the recommended resources in order to self study about it?
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Applying Discrete Filters

I have an exercise in DSP. I learnt about discrete filter but I don't know how to apply it to produce an output from an input signal. Please guide me to do this: Assume fundamental sample time is 1 ...
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Confusion regarding DFT calculation?

I am studying Richard lyon chap3 , article "Understanding the DFT equation " But i am bit confused how x(n) is calculated specially x(0) and x(1) because apparently x(n) is calculated by plugging ...
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performing FFT on Voltage measurments to get Z(f)

I have a csv file containing measurments a system's step response when the step is current and the output is the voltage. output looks something like this and the it's evenly sampled provided I know ...
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1answer
231 views

how to create a DFT with scalloping/spectal leakage

I had some problems with scalloping and spectral leakage. I think I solved that. I wrote an algorithm in C++ using FFTW3. It works. But now I want to show when you get scalloping. It took me some ...
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266 views

How Can I practically implement the FFT with size unequal to a power of two?

Can anybody explain how I can implement the Fast Fourier Transform (FFT) of length unequal to a power of two in hardware, e.g. FPGA? What is the algorithm for this implementation? Does anybody know ...
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2answers
143 views

Can digital filters actually separate signals?

I've come to realize what appears to be a hard limit in convolution theorem: to avoid time-domain aliasing, we must pad the signal/filter, but the padding distorts the spectrum. Consider a ...
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1answer
146 views

frequency domain vs cosine wave amplitude

Hey guys, what is the difference between b.) and c.)? Why do we need each of them? Excrept from: http://www.dspguide.com/ch8/5.htm (scroll below)
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The mathematical interpretation of DFT [closed]

We have the DFT(matrix form) $X = Wx$ ($W$ is the Fourier basis matrix, $x$ is the original signal in time domain, $X$ is in the frequency domain). In mathematics, $x$ represents the coordinates of $...

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