All Questions

65
votes
2answers
19k views

Why is it a bad idea to filter by zeroing out FFT bins?

It's very easy to filter a signal by performing an FFT on it, zeroing out some of the bins, and then performing an IFFT. For instance: ...
106
votes
6answers
57k views

What does frequency domain denote in case of images?

I was just learning about the frequency domain in images. I can understand the frequency spectrum in case of waves. It denotes what frequencies are present in a wave. If we draw the frequency ...
28
votes
6answers
45k views

Understanding the Matched Filter

I have a question about matched filtering. Does the matched filter maximise the SNR at the moment of decision only? As far as I understand, if you put, say, NRZ through a matched filter, the SNR ...
70
votes
6answers
131k views

Why should I zero-pad a signal before taking the Fourier transform?

In an answer to a previous question, it was stated that one should zero-pad the input signals (add zeros to the end so that at least half of the wave is "blank") What's the reason for this?
4
votes
1answer
838 views

Compensating Loudspeaker frequency response in an audio signal

I have been working on a project in which I was required to work on the audio signals recorded from the loudspeaker kept in front of a filter. So, to simply explain it: $$\boxed{\rm LoudSpeaker} \...
9
votes
2answers
1k views

How to deal with low fundamental when using AMDF for pitch extraction?

I am using the Average Magnitude Difference Function to estimate the fundamental frequency of a quasi-periodic audio signal. The AMDF is defined as $$ D_n = \frac{1}{N-n}\sum_{k=n}^{N-1}|S_k - S_{k-n}...
16
votes
3answers
55k views

Variance of White Gaussian Noise

It could seem an easy question and without any doubts it is but I'm trying to calculate the variance of white Gaussian noise without any result. The power spectral density (PSD) of additive white ...
32
votes
13answers
15k views

What Resources Are Recommended for an Introduction to Signal Processing (DSP)?

What are some recommended resources (books, tutorials, lectures, etc.) on digital signal processing, and how to begin working with it on a technical level?
22
votes
1answer
44k views

Kalman filter for position and velocity: introducing speed estimates

Thanks to everyone who posted comments/answers to my query yesterday (Implementing a Kalman filter for position, velocity, acceleration ). I've been looking at what was recommended, and in particular ...
24
votes
6answers
13k views

Flipping the impulse response in convolution

During convolution on a signal, why do we need to flip the impulse response during the process?
4
votes
4answers
2k views

About Discrete Fourier Transform vs. Discrete Fourier Series

I am new to the field of signal processing. I am wondering what is the difference between DFS(Fourier Series) vs. DFT(Fourier Transform). For common applications, usually we get a segment(length <...
14
votes
2answers
25k views

How do I manually plot the frequency response of a bandpass Butterworth filter in MATLAB without freqz function?

I have code like below that applies a bandpass filter onto a signal. I am quite a noob at DSP and I want to understand what is going on behind the scenes before I proceed. To do this, I want to know ...
19
votes
4answers
20k views

How many taps does an FIR filter need?

I am looking to design a set of FIR filters to implement a low pass filter. I am also trying to reduce the latency of the signal through the filter so I am wondering what the minimum number of taps I ...
50
votes
2answers
24k views

Why so many methods of computing PSD?

Welch's method has been my go-to algorithm for computing power spectral density (PSD) of evenly-sampled timeseries. I noticed that there are many other methods for computing PSD. For example, in ...
34
votes
3answers
52k views

Why is the FFT “mirrored”?

If you do an FFT plot of a simple signal, like: t = 0:0.01:1 ; N = max(size(t)); x = 1 + sin( 2*pi*t ) ; y = abs( fft( x ) ) ; stem( N*t, y ) 1Hz sinusoid + DC ...
5
votes
2answers
5k views

Frequency shifting of a quadrature mixed signal

I've a quadrature mixed signal with 10 MHz as highest frequency available. I want to shift it to any frequency lesser than 10 MHz. I should get it by multiplying this signal by cosine of the required ...
127
votes
8answers
119k views

Why is the Fourier transform so important?

Everyone discusses the Fourier transform when discussing signal processing. Why is it so important to signal processing and what does it tell us about the signal? Does it only apply to digital signal ...
77
votes
9answers
64k views

What is the physical significance of negative frequencies?

This has been one of the holes in my cheddar cheese block of understanding DSP, so what is the physical interpretation of having a negative frequency? If you have a physical tone at some frequency ...
28
votes
1answer
6k views

Does the autocorrelation function completely describe a stochastic process?

Is a stochastic process completely described by its autocorrelation function? If not, which additional properties would be needed?
17
votes
3answers
8k views

How to implement a digital oscillator?

I have a floating-point digital signal processing system that operates at a fixed sample rate of $f_s = 32768$ samples per second implemented using an x86-64 processor. Assuming that the DSP system ...
9
votes
1answer
19k views

I and Q components and the difference between QPSK and 4QAM

Both 4QAM and QPSK apparently produce the same waveform, but are they the same mathematically? In a QPSK constellation, are the mapping points at 45, 135, 225 and 315 degrees while the 4QAM is at 0, ...
12
votes
2answers
7k views

What are advantages of having higher sampling rate of a signal?

Being a non signal processing science student I have limited understanding of the concepts. I have a continuous periodic bearing faulty signal (with time amplitudes) which are sampled at $12\textrm{ ...
9
votes
1answer
2k views

What is an AMDF?

The wikipedia page for Average Magnitude Difference Function/Formula (AMDF) appears to be empty. What is an AMDF? What are AMDF's properties? What are AMDF's strengths and weaknesses, as compared ...
5
votes
2answers
14k views

Transfer function of second order notch filter

Can anyone mention the transfer function of second order notch filter to remove the line frequency of 50 Hz, in terms of frequency and sampling rate. Just like for Low pass Butterworth filter as, $$ ...
4
votes
1answer
2k views

What happens when N increases in N-point DFT [duplicate]

I am curious about DFT, and I wrote a simple MATLAB code to test what happens when $N$ increases. I took a rectangular signal with length $L=15$, an then found th DFT of 16, 32 and 64 points. I looked ...
1
vote
3answers
3k views

how to make CIC compensation filter

I gotta wrap my head around to design CIC compensation filter I'm studying by referring these materials: Altera, "Understanding CIC compensation filters Hardware Efficient FIR Compensation Filter ...
66
votes
4answers
171k views

What is meant by a system's “impulse response” and “frequency response?”

Can anyone state the difference between frequency response and impulse response in simple English?
54
votes
7answers
84k views

How do I implement cross-correlation to prove two audio files are similar?

I have to do cross correlation of two audio file to prove they are similar. I have taken the FFT of the two audio files and have their power spectrum values in separate arrays. How should I proceed ...
8
votes
10answers
29k views

Deconvolution of 1D Signals Blurred by Gaussian Kernel

I have convolved a random signal with a a Gaussian and added noise (Poisson noise in this case) to generate a noisy signal. Now I would like to deconvolve this noisy signal to extract the original ...
20
votes
2answers
39k views

Step by Step Camera Pose Estimation for Visual Tracking and Planar Markers

I have been working on the topic of camera pose estimation for augmented reality and visual tracking applications for a while and I think that although there is a lot of detailed information on the ...
35
votes
3answers
40k views

What are the most common algorithms for adaptive thresholding?

Adaptive thresholding has been discussed in a few questions earlier: Adaptive Thresholding for liver segmentation using Matlab What are the best algorithms for document image thresholding in this ...
24
votes
4answers
4k views

Which time-frequency coefficients does the Wavelet transform compute?

The Fast Fourier Transform takes $\mathcal O(N \log N)$ operations, while the Fast Wavelet Transform takes $\mathcal O(N)$. But what, specifically, does the FWT compute? Although they are often ...
1
vote
1answer
2k views

Numerically Controlled Oscillator (NCO) for phasor implementation?

If I want to simulate a digital oscillator (or phasor) to modulate an arbitrarily length signal: $$y(t) = \cos(2\pi f_ct)\quad\text{where}\quad t = \frac{n}{f_s}\quad\text{for sample}\quad n$$ What ...
44
votes
3answers
19k views

What algorithm does Google use for its “Search By Image” site?

What is your best guess how Google Image Search works? I can upload a photo and can search for similar images. What algorithm does it use to identify similar images?
37
votes
6answers
41k views

What is the distinction between ergodic and stationary?

I have trouble distinguishing between these two concepts. This is my understanding so far. A stationary process is a stochastic process whose statistical properties do not change with time. For a ...
29
votes
2answers
26k views

What is the advantage of MATLAB's filtfilt

MATLAB's filtfilt does a forward-backward filtering, i.e., filter, reverse the signal, filter again and then reverse again. Apparently this done to reduce phase ...
25
votes
5answers
15k views

How to create a sine wave generator that can smoothly transition between frequencies

I am able to write a basic sine wave generator for audio, but I want it to be able to smoothly transition from one frequency to another. If I just stop generating one frequency and immediately switch ...
10
votes
3answers
11k views

How to resample audio using FFT or DFT

I'm down sampling voice audio by first performing an FFT, then only taking the parts of the result that I need, and then performing an inverse FFT. However, it's only working properly when I'm using ...
6
votes
1answer
1k views

Location of Matched Filter

In a digital communication receiver, matched filter(SRRC filter) is used. In different literatures, the location of the matched filter is mentioned in two different places. One is just after the ADC ...
3
votes
2answers
2k views

Noise detection

I was wondering if someone could suggest a method to differenciate between two signals, on algorithmic scale for example a criterium to calculate, that shows how noisy a signal is, i have found a post ...
4
votes
3answers
564 views

Is there a condition for bandpass sampling?

Consider a signal that has lowest frequency component $F_l$ and highest frequency component $F_h$. According to the theory of bandpass sampling, this signal can be sampled and succesfully recoverd if ...
29
votes
6answers
4k views

What is the most lucid, intuitive explanation for the various FTs - CFT, DFT, DTFT and the Fourier Series?

Even after having studied these for quite sometime, I tend to forget [if I'm out of touch for a while] how they are related to each other and what each stands for [since they have such similar ...
45
votes
16answers
122k views

What is the physical meaning of the convolution of two signals?

If we convolve 2 signals we get a third signal. What does this third signal represent in relation to the input signals?
45
votes
4answers
41k views

What is the difference between convolution and cross-correlation?

I've found on multiple sites that convolution and cross-correlation are similar (including the tag wiki for convolution), but I didn't find anywhere how they differ. What is the difference between ...
26
votes
7answers
20k views

What is an algorithm to re-sample from a variable rate to a fixed rate?

I have a sensor that reports its readings with a time stamp and a value. However, it does not generate readings at a fixed rate. I find the variable rate data difficult to deal with. Most filters ...
45
votes
10answers
29k views

Algorithm(s) to mix audio signals without clipping

I'd like to mix two or more PCM audio channels (eg recorded samples) digitally in an acoustically-faithful manner, preferably in near-real-time (meaning little or no peek-ahead). The physically "...
16
votes
3answers
42k views

FIR filter with linear phase, 4 types

I know there are 4 types of FIR filters with linear phase, i.e. constant group delay: (M = length of impulse response) Impulse response symmetrical, M = odd Imp. resp. symmetrical, M = even Imp. resp....
15
votes
1answer
707 views

Is the Laplace transform redundant?

The Laplace transform is a generalization of the Fourier transform since the Fourier transform is the Laplace transform for $s = j\omega$ (i.e. $s$ is a pure imaginary number = zero real part of $s$). ...
10
votes
1answer
2k views

Understanding multirate filtering fundamentals

I am having trouble grasping some of the fundamental concepts of multirate filtering. I see from various sources that the basic building blocks of a multirate filter are the dyadic analysis and ...
0
votes
1answer
17k views

Deriving SER & BER for 4QAM, 16QAM and 32QAM

Required to find symbol error rate vs $\dfrac{E_b}{N_0}$ for 4QAM, 16QAM & 32QAM. Thought that SER & BER are the same but did my research to find that BER is $\dfrac{1}{\log_2(M)}$ of SER...(...

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