The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in the frequency and time domains. DFT requires an input function which is discrete and non-zero, such as a sampling from an analogue audio signal.

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Using Goertzel Algorithm in under-sampling

I plan to calculate a signal's phase using Goertzel Algorithm. I have 2 signals coming to microcontroller's ADC. Need to measure the phase difference between them. Signals are 15MHz sinusoids. Sample ...
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39 views

image 2-d real cepstrum with DFT ? ifftshift needed?

this is my testing image,it is taken from this paper: I tried to transform it into its real cepstrum domain with this simple matlab code: cepstrum_img=ifft2(log(1+abs(fft2(img(:,:,1))))); ...
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85 views

Extraction of fundamental signal information-Fourier full cycle algorithm

After filtering my noisy input signal using an anti-aliasing and FIR filter, I now wish to get the basic signal information (peak voltage and impedance; $R$ and $X$) from the pre-filtered as well as ...
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50 views

Simple questions related to dft

I'm reading a book about dsp and doing some exercises. Here is question that confused me: A peak appears at index number 19 when a 256 point DFT is taken of a signal 1) What is the frequency of the ...
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37 views

Calculating Energy Spectral Density from Magnitude and Phase data

I'm trying to do a program that can judge whether 2 audio files have the same pronunciation or not by comparing the frequency of them with each other. The first step, finding the magnitude and phase ...
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59 views

Signal Resolution

I have a question. Suppose we have a signal $x(n)$, length (samples) $N=400$ which have been sampled with $f_s=8000 \mathtt{Hz}$. Also suppose $X(k)$ - the DFT transform of this signal. How many ...
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1answer
72 views

Uncertainty, time-bandwidth product, harmonics

For a signal that is not corrupted with noise, how is the time-bandwidth product affecting the uncertainty or error introduced when extracting the fundamental frequency ? I mean, instead of choosing ...
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1answer
50 views

Understanding IIR , Low Pass, High Pass, Chebyshev, Elliptic Filter? [closed]

I see these terms everyday in every lecture, I do read stuff from wikipedia, follow lecture notes, study solved exercises. All in all I do have a rough idea about these, I know a little from ...
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1answer
47 views

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 ...
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1answer
117 views

Time domain distortion vs Harmonics

I have a periodic time domain sensor signal sampled at $500 \text{ Hz}$ whose amplitude spectrum I compute and obtain. From the periodicity of the signal, I was expecting the fundamental frequency to ...
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1answer
40 views

Polarity inversion in frequency domain (polar coordinates)

I don't fully grasp how polarity inversion is performed in the polar coordinates of frequency domain. The frequency components of the signal do not change, so the amplitude part is going to stay ...
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2answers
48 views

Hermitian symmetry in OFDM systems

I am trying to understand the usage of Hermitian symmetry in OFDM systems and have a couple of questions regarding this. What is the reason of using the Hermitian symmetry in OFDM? How can we ...
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40 views

Reason of circular conv in OFDM

In OFDM system, after IFFT a CP is added at the beginning of the OFDM symbol by copying it from the end of the symbol.My question is that with CP why we use cyclic convolution instead of linear ...
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1answer
57 views

Determining power of white noise component of an incomplete time signal

I want to determine the power of the noise component of a time dependend signal x(t) (similar to picture below) With constant sampling rate I use Parceval's Therorem and calculate the standard ...
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1answer
140 views

Why can't DFT be used when samples are not equally spaced in time?

I found the following comment here The DTFT can be used when the samples are not equally spaced in time, the DFT cannot My initial thought was that this had to do with periodicity of the basis ...
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1answer
28 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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66 views

Autocorrelation Function and Power Spectrum

My aim is to determine the power spectrum of a signal of finite duration using Its autocorrelation function Performing FFT directly on the time-domain data The function is defined as follows in ...
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2answers
81 views

Magnitude Spectrum, different magnitudes same amplitude

When the following code is written,the resulting magnitude spectrum shows magnitude values represented by two peaks is different even though they have the same amplitude. why is that? a fast reply ...
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3answers
56 views

Upper bound for the FFT coefficients of a bounded signal

I have a discrete signal $x[n]$ of length say 1024, such that : $$-1 \leq x[n] \leq 1, \qquad for \ all \ n,$$ and let $y[k]$ be its DFT. Is there an upper bound for $|y[k]|$ ? (i.e. for the ...
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1answer
89 views

Correlation between real and imaginary parts of a Fourier transform of zero mean Gaussian

From this previous post, the real and imaginary parts of the Fourier transform of a zero mean Gaussian are uncorrelated (and i.i.d. Gaussians) This some how seems counter-intuitive. It seems if the ...
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1answer
50 views

Discrete Fourier Transform - measuring signal at equi-spaced points

I found a really intuitive explanation of Discrete Fourier Transform here. To summarize the author's approach briefly : What if any signal could be made from circular motion (repeating cycles) ? ...
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2answers
108 views

Why would you use DCT as oppose to DFT for detecting oscillation in a signal?

For my project, I needed to detect the primary oscillation frequency in a signal data. As I googled around, it turns out that DCT is the best tool to find this ...
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1answer
108 views

How can I reduce noise errors when detecting DTMF with the Goertzel algorithm?

Thanks a lot to whoever downvoted my question for no good reason. I wrote an implementation of the Goertzel algorithm in JavaScript and made a demo that detects DTMF dial-tones. You can find the ...
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35 views

DFT method for a sequence defined by recursion

I encountered the following interesting computational problem in the field of computational statistical mechanics. https://www.dropbox.com/s/8yimd9uy5u0jrdj/dftpr.pdf thank you :)
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2answers
100 views

DFT for something similar to convolution

I have the following problem: Let $x$, $y$ be finite real valued sequences defined on $0 \ldots N-1$ and let $g$ be a non negative integer. Define: also on $0 \ldots N-1$. Note that the sum is ...
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1answer
30 views

Matrix form of STFT

IS there a Matrix form of the STFT that could be applied to a signal directly, as in the case of DFT? We know the matrix structure of the DFT Matrix. Can we derive that somehow for a STFT Transform? ...
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45 views

2D version of Shift Theorem

What is the 2D version of Shift Theorem?
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30 views

Meaning of tight frame in the context of texture synthesis

I am currently reading "A parametric texture model based on joint statistics of complex wavelet coefficients", by Portilla and Simoncelli. In this article, they use the "steerable pyramid" to ...
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2answers
46 views

Complex numbers in a frequency domain of a 2D image [duplicate]

I am try to grasp the idea of frequency domain for images. I think get the basics, but now I've stuck with a question that I can't find appropriate answer anywhere. How are frequency domain and ...
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2answers
101 views

Intro Question to Signal Processing (Low-Pass Filter)

I have a noisy signal file in Matlab and I have to denoise the polluted signal using a discrete Fourier transform. I'm asked to perform the fourier transform, then take its absolute value. Then ...
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1answer
84 views

How can I use time-series transforms for detecting malware? [closed]

I am student of network security, and very unfamiliar with the domain of signal processing. Do pardon my naivety at asking very basic stuff. My work deals with detecting malicious activity in network ...
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78 views

discrete fourier transform in Matlab - theoretical confusion

I have a periodic term $V(x) = \sum_K \exp(iKx) V_K$ where $K =2\pi n/a$ where $a$ is the periodicity of the term and $n =0,1,2,3....$ Now I want to find the Fourier coefficient $V_K$ corresponding ...
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1answer
102 views

Scaling Property in DFT

In below image, we have scaling property of DFT, how the final equation is obtained from the above equation. That is how we are getting the scaling factor , $ \frac{1}{|ab|} $ in the final equation ? ...
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1answer
43 views

Standard representation of FFT of an Image?

Statement 1 : When we take DFT of an image matrix, we get DFT co-efficient matrix. What does the DFT Co-efficients tells about the image? (For example, take the 1st co-eff in the DFT matrix, what ...
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1answer
132 views

FFT analysis of longer data sets

I have a problem with a FFT analysis in MATLAB, which is probably related to my limited understanding of the fundamentals of Fourier analysis. I use MATLAB’s built-in fft analysis function. The ...
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1answer
93 views

How to evaluate expressions without explicitly computing a discrete fourier transform?

Hello DSP guru nation, I am trying to learn this part but I dont seem to understand. if I have a finite length sequence, and a n-point DFT of it (in an interval)... is it possible to evaluate ...
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0answers
48 views

Using Spectral Density To Compute The Autocorrelation Function

I have a spectral density function $S_{xx}$ and I want to compute the discrete autocorrelation function $r_{xx}[n]$ from it but I can seem to figure out how.I have $$ S_{xx} = 3e^{-2jw} + ...
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2answers
188 views

Is $O (N \log N)$ FFT speed the fastest we can ever attain?

I am wondering about whether or not there is a theoretical limit as to the speed at which we can compute a DFT. We all know that the FFT executes in $O (N \log N)$ time. However, is this a lower bound ...
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2answers
89 views

STFT - DFT size of the bins

Having some trouble understanding this concept, really could do with some advice. I want my STFT to have the following parameters: NFFT = 256 ...
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1answer
87 views

Change of bin magnitude when phase of signal changes when doing FFT?

I am working on an implementation in which I need to apply an FFT to determine which of 4 frequencies are present in a signal. I am doing a 64 point FFT on a buffer which only is partly filled (the ...
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2answers
124 views

Analyse audio/music frequencies without STFT, at 1/f temporal resolution, using probe phasors at logarithmically-spaced frequencies, O(N log N)?

First, some background: The STFT is the best general-purpose tool I know of for analysing a (musical or other) signal into its component frequencies. For many purposes the STFT works fine, but there ...
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2answers
117 views

DFT Vs DCT - spectrum differences

When you are transforming a signal in to a frequency domain using both DFT and DCT, say for a function sin(x), how the spectrum will be? will both frequency values (of DCT and DFT) same? Can anyone ...
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1answer
63 views

How do I compute the DC component given the other part of the Fourier spectrum?

I often see examples in textbooks where someone constructs a 2D Fourier spectrum of an image by fixing two (symmetric) pixels to a given value, and computes the inverse DFT to get a nice waveform ...
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1answer
120 views

How to compute the statistics of the DFT of noise?

I would like to know how to compute the statistics of the discrete Fourier transform of a noise signal. To illustrate what I mean, I will first explain in detail a computation I have managed to do ...
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5answers
146 views

To what extent can we see signals that fall between frequency bins?

I have a simple problem I would like to figure out for fourier analysis of seismic data. Let us say that we have a signal $z[n]$, of length $N$. If I take its (same size) FFT, I will get $Z[k]$, ...
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1answer
85 views

Squared dft Coefficient defines?

What does the squared magnitude of the DFT coeffiecient tell me, where do I use it? what does it define? $|X(k)^2| = ???$ I am curious to know because the Amplitude is given by the formula $A_k ...
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1answer
121 views

Why is it possible to frequency sweep with just one sinusoid?

One way to measure the frequency response of a filter is to input separate cosine/sine wave at the desired frequency, measure the steady state output, stack the inputs/outputs into complex arrays, and ...
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151 views

Discrete Fourier transform

When you perform a discrete Fourier transform (DFT), and compute the DFT coefficients, $c_k$ and $X(K)$, what do these values tell us about the signal it came from?
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64 views

Using goertzel confuses me

I am having some troubles understanding the algorithm. My algorithm looks like this. how come am i able to compute the DFT coefficient using this algoritm. As far as i know $$ X[k] = ...
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1answer
126 views

Goertzel algorithm

I am having a hard time understanding why my textbook takes the squared magnitude of the calculated DFT coefficients. I know in DFT, you would normally take the magnitude to get the spectrum, how ...