Tagged Questions

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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27 views

Filter design using inverse dft

How do I get the cut-off frequency? A filter is needed to recover $x_2(n)$ from the signal: $$x(n) = x_1(n) + x_2(n) + x_3(n)$$ where: $x_1(n) = \sin(0.5n)$ $x_2(n) = \sin(1.4n)$ ...
0
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0answers
20 views

2D FFT vs 2 Pass 1D FTT

We know that the 2D FFT can be performed by taking the FT along the rows and then taking the FT along the columns. I'm wondering how theoretical performance compares to the direct 2D FT case, which ...
0
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0answers
31 views

DFT of a pressure signal from space domain to wavenumber domain

When I do the DFT of the following signal: I get the following DFT which doesn't capture any peaks at all: Why is this? I'm not really able to identify what the error is?
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0answers
28 views

Size obtained by applying Linear convolution

We know that applying a filter on an image is called correlation or convolution depending on the filter angle. In Gonzalez I have read that we can apply linear convolution on an image. Here I have a ...
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1answer
100 views

Cooley-Tukey Implementation of FFT in Matlab

For my course I need to implement a 30 point Cooley-Tukey DFT by transforming it into a 5x6 matrix. I have tried to implement using the following Matlab code: ...
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2answers
59 views

Purpose of Phase Information

I am learning Fourier Transform from many days but till now I am not able to understand what does phase angle image show us or tell us? They say that MAGNITUDE tells "how much" of a certain frequency ...
0
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1answer
31 views

Frequency of the wave in frequency domain

If we have a 1-dimensional wave in time domain, it can be represented in frequency domain with x axis indicating the frequency of the wave and y axis indicating amplitude/magnitude of the wave. But ...
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1answer
50 views

Explain Shift property of DFT

Please check the link What effect does a delay in the time domain have in the frequency domain? Here it is said that if you delay your input signal by D samples, then each complex value in ...
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2answers
37 views

What is a translation property in DFT

Hi someone please explain me the translation property of DFT. I am not able to understand it neither from Gonzalez nor from internet. I have done extensive study on this but not able to get it. Really ...
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1answer
42 views

What is the significance of the DFT in SC-FDMA systems?

Long term evolution (LTE) systems use single-carrier frequency division multiplex (SC-FDMA) in the uplink. In such a system, there is a DFT block and a sub carrier mapping block before the IFFT block. ...
1
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1answer
83 views

Recursive version of DFT as presented in Cooley-Tukey paper

The seminal paper of Cooley and Tukey provides an iterative method for computing the DFT for a sequence of length $N$. Specifically, they mention a method which utilizes the fact that $N$ can be ...
0
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1answer
21 views

Determining effect of powers of DFT matrix conjugate on input without multiplying

Suppose I have a DFT matrix $F$ of dimensions $N \times N$ where $N$ is a power of $2$. I convert it into a unitary matrix $\displaystyle U = \frac{F}{\sqrt{N}}$ and compute $S = U^* U^* $. $S$ ...
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0answers
21 views

Variation in Signal Power in Mimo system

I am exploring methods for reducing computations required by MUSIC (Multiple Signal Classification) Algorithm. Most of the computational power is spent on calculating SVD. My approach is to take ...
3
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0answers
49 views

Incorrect Frequency results when using Multiple Signal Classification (MUSIC)

I am using MUSIC (Multiple Signal Classification) to determine Direction Of Arrival (DOA) and frequency of signals impinging on an Antenna Array. I am using a function ...
0
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1answer
31 views

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 ...
0
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0answers
61 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 ...
0
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0answers
41 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 ...
1
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0answers
42 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
103 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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2answers
118 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 ...
3
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5answers
145 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 ...
2
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2answers
89 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 ...
0
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1answer
52 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
480 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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0answers
58 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 ...
1
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1answer
58 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 ...
1
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1answer
74 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 ...
2
votes
2answers
140 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 ...
0
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1answer
50 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))))); ...
1
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0answers
106 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 ...
0
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1answer
87 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 ...
0
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0answers
42 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 ...
0
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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 ...
0
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1answer
92 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 ...
0
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1answer
57 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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votes
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 ...
3
votes
1answer
129 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 ...
1
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1answer
56 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 ...
1
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2answers
99 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 ...
0
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2answers
63 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
votes
1answer
68 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
votes
1answer
167 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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votes
1answer
40 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.
0
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0answers
115 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 ...
0
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2answers
175 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 ...
0
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3answers
64 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
votes
1answer
137 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 ...
1
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1answer
78 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) ? ...
2
votes
2answers
134 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
190 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 ...