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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Interpreting magnitude of DFT results

I'm working on creating a simple program to render spectrograms like this one. In this plot, the X-axis is time, the Y-axis is frequency, and the color represents the magnitude of the DFT at that ...
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38 views

Autocorrelation and FFT : avoid zero-padding

Some posts evocate the computation of convolution or cross-correlation using FFT and zero-padding the temporal signal. I want to compute the autocorrelation of a 3D array using FFTW (2 dimensions are ...
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25 views

Instantaneous power estimation by discrete hilbert transform - how far does it smooth?

In my research area, instantaneous power in a specific frequency band is commonly estimated by the following procedure: Apply a bandpass filter on the raw signal (e.g. 80-90Hz bandpass). Estimate ...
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26 views

Multiply filter kernel by sine

1)Suppose that we have low-pass filter with cf equal to 0.1. How frequency response would look like if I multiply filter kernel by sine with frequency say 0.3? How this is related to converting ...
2
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2answers
98 views

please give the reason why every notation for DFT is valid?

$X$ represents sample in frequency domain and $x$ represents samples in time domain. NOTATION 1 $ X[k] = \sum\limits_{n=0}^{N-1} x[n] \ e^{-j \frac{2\pi}{N} n k} $ $ x[n] = \frac{1}{N} ...
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3answers
105 views

About frequency resolution [duplicate]

The frequency resolution of DFT is $\Delta f = \frac{1}{T_{0}} = \frac{1}{NT} = \frac{f_{s}}{N}$ where $f_{s}$ is sampling frequency, $T_{0}$ is sampling time, $N$ is number samples, and $T$ is the ...
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5answers
137 views

Why does the DFT assume the transformed signal is periodic?

In many signal processing books, it is claimed that the DFT assumes the transformed signal to be periodic (and that this is the reason why spectral leakage for example may occur). Now, if you look at ...
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2answers
73 views

Difference between convolution and multiplication of freq. response and freq. spectrum

Suppose I have impulse response like [1/25,2/25,3/25,4/25,5/25,4/25,3/25,2/25,1/25]. I did convolution with 600 samples of test signal (it seems that I did some filtering). Then I calculated the ...
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29 views

How is the frequency resolution formula derived? [duplicate]

How is the frequency resolution formula derived? I know it is $\displaystyle\frac{N}{f_{s}}$ but I don't understand how it is related to the DFT.
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1answer
29 views

Basics of waveform, how to define the zero point

Audio is a sequence of waveforms which have peaks, troughs, 0, just like below. How to define the x axis (y = 0) in the picture, how to choose the 0 point in the waveform since there are so many ...
3
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3answers
457 views

disadvantages of FFT, it can not extract enough frequencies without enough samples

Let's say sampling rate is $Fs = 44\mathtt{kHz}$, now I have $N = 2048$ samples, then I can get $N/2 + 1 = 1025$ frequencies. I'm confused by Matlab's FFT documentation that says the frequencies are ...
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41 views

Using Fourier Transform on Gyroscope

The original idea is to calculate distance from accelerometer input. However, accelerometer reading also contains the gravitational values, thus to remove gravity, I tried using Gyroscope. The idea ...
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1answer
47 views

Exercise related to frequency resolution and SNR

I'm studying a book aboud dsp and trying to make excercises. Here is one I'm interested in: A scientist acquires 65,536 samples from an experiment at a sampling rate of 1 MHz. He knows that the ...
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1answer
72 views

Writing a Discrete Fourier Transform program

I would like to write a DFT program using FFT. This is actually used for very large matrix-vector multiplication (10^8 * 10^8), which is simplified to a vector-to-vector convolution, and further ...
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2answers
98 views

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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1answer
43 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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0answers
92 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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1answer
80 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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41 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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2answers
64 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
78 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
55 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
50 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
122 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
45 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
63 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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2answers
43 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 ...
2
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1answer
65 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 ...
4
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1answer
157 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
32 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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80 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
108 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
60 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 ...
2
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1answer
96 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
71 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
121 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
143 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
113 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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50 views

2D version of Shift Theorem

What is the 2D version of Shift Theorem?
4
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36 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
107 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
90 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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0answers
81 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
122 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 ? ...
2
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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
148 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
96 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 ...