15 votes
Accepted

Intuitive explanation of cross-correlation in frequency domain

The concept is based on the convolution theorem, which states that for two signals $x(t)$ and $y(t)$, the product of their Fourier transforms $X(f)$ and $Y(f)$ is equal to the Fourier transform of the ...
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8 votes

Verifying Channel Response Identity

I think you made a mistake between the power spectrum and the Fourier Transform. This is the right form of the Convolution Theory (Nothing is squared): $$ \lvert Y(\omega)\rvert = \lvert H(\omega) X(\...
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8 votes
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Does sampling in the frequency domain cause time-domain aliasing?

The answer is: yes, sampling in the frequency domain causes aliasing in the time domain, exactly like the dual case: sampling in the time domain causes aliasing in the frequency domain. There are ...
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  • 80.4k
7 votes

Under what condition is the available bandwidth $f_s$ instead of $\frac{f_s}{2}$?

If your signal is real-valued, then it's spectrum is conjugate symmetric. That means, that negative frequencies (or frequencies from $\frac{f_s}{2}$ up to $f_s$) are mirrored. Thus we can always ...
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  • 10.5k
6 votes

DSP interview question: use of the identity in development of a significant transform

This is related to Chirp Z-transform (CZT) (refer to the Bluestein's algorithm). Using this identity, the CZT can be expressed in terms of a convolution. Hence, it can be efficiently implemented using ...
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  • 4,115
6 votes
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Dual-Tone Multi Frequency signalling

Essentially, the reason why you need two tones is to ensure that a normal human voice can't replicate the tones. As such, by simultaneously generating a tone from a high-frequency group and low-...
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  • 513
6 votes

Upsampling by zero padding or duplicating sequence

Matlab’s ‘upsample()’ command does not “pad” a sequence with zero-valued samples. The ‘upsample()’ command “stuffs” a sequence with zero-valued samples. “Zero padding” and “zero stuffing” are two ...
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6 votes

What does 'canonical' mean?

A canonical implementation of a digital filter has the minimum number of delay elements. The same filter cannot be implemented with less memory. Since memory is often not the only concern, a canonical ...
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6 votes
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What does 'canonical' mean?

The etymology refers to the canon, as a rule or a body of rules, or axiomatic or universal standards. It exists in arts: sculpture, music, script writing, etc. The notion of canon law is also used in ...
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5 votes
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Real-time block processing setup on ARM

First, use a timer and an ISR to get accurate timing (don't forget to configure the NVIC so that this timer interrupt takes over any other ISR that would be running). Only this will ensure a ...
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5 votes

How can define an indicator which measures the degree of similarity between two signals?

The general topic of finding similarities between signals is wide ranging: are the signals of same sampling, length, offset, shift or scale? where do they take their values (discrete, real, complex)?...
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5 votes
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Problems with implementation of a band-stop filter on an MCU (dsPIC) using fixed-point arithmetic

The denominator (recursive coefficients Ai) look OK: the poles of your system are at 45 degree angles ($\pi/4$), with magnitude 0.68 (which is not very aggressive for a notch filter; in my opinion ...
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5 votes
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What's the difference between a DSP and microcontroller?

a Digital Signal Processor is one that has, in its instruction set, some instructions and addressing modes that are optimized for processing digital signals. usually these optimizations can be shown ...
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5 votes

DSP with 8+ inputs for simple beamforming

8+ high quality inputs for beamfroming and "...beginner friendly..." are competing requirements. There will soon be the audioinjector which attaches on Raspberry Pi and would be a relatively ...
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  • 10.1k
5 votes

What is so special about this filter coef = [1,2,1]?

It is a symmetric odd-sized FIR smoothing kernel, belonging to the class of Pascal or binomial filters that somehow sample a Gaussian kernel. Plus, its coefficients are simple dyadic integers, that ...
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5 votes

How to Improve Signal Processing Skills?

One of the best ways is to hang out on this community. Read questions and answers. Try to replicate results on answers. Once you have more knowledge, try answering questions of others. If you ...
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  • 41.3k
5 votes

Career in signal processing

I myself recently graduated from Applied Mathematics and began PhD in signal processing. I do Stochastic Geometry modeling of wireless networks in particular, which is quite mathematical subject. It ...
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  • 146
4 votes
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Verifying Channel Response Identity

Just change the code to the following: ...
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  • 10.5k
4 votes
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What is meant by Impulse Response

Suppose you have given an input signal to a system: $$ x(n)=\begin{cases} 1, & \mbox{if } n=0 \\ 0, & \mbox{if } n\ne 0 \end{cases} $$ Then the output response of that system is known as ...
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4 votes
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IIR Filter - calculating the phase response

Finding the phase response of a biquad at a specific frequency is simple. Recall the transfer function of a biquad: $$ H(z) = \frac{b_0 + b_1z^{-1} + b_2z^{-2}}{a_0 + a_1z^{-1} + a_2z^{-2}} $$ The ...
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4 votes
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Stereo Widening

This code is splitting a stereo signal with left and right components into a stereo signal with mid and side components, scaling the mid and side components and converting back to left and right ...
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  • 827
4 votes
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How can define an indicator which measures the degree of similarity between two signals?

assuming finite power signals: $$ \lVert x \rVert^2 \triangleq \lim_{N \to \infty} \ \frac{1}{2N+1} \sum\limits_{n=-N}^{+N} \big|x[n] \big|^2 \ < +\infty $$ this is a Hilbert Space sorta thingie. ...
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4 votes

How can define an indicator which measures the degree of similarity between two signals?

if you are searching for similarity between two signals in frequency domain, you can go for coherence. Coherence indicates frequency components common to both signals
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4 votes

Compression Sensing for Blind Source Separation

I will sketch an idea how to use Sparse Represenattion (Dictionary Learning) for BSS. Let's say we have $ \mathcal{S} = \mathcal{S}_{1} \cup \mathcal{S}_{2} $ where $ \mathcal{S}_{1} = \left\{ {x}_{i}...
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4 votes
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What applications do DSP processors primarily target?

For example, if I'm doing audio processing, wouldn't I just be better off using x86 since that has a larger install base? "Larger" is a good word for the x86. It needs a larger space claim ...
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  • 8,638
3 votes

Get a N-FFT with two N/2-FFT already computed

You can compute a length $N$ FFT from two length $N/2$ FFTs of consecutive parts of the data, but it can't be done efficiently, i.e. it is more efficient to go back to the time domain, combine the ...
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  • 80.4k
3 votes
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convolution of a real and complex signal

You are confusing several different notions. First of all, two signals $x(t)$ and $y(t)$ are orthogonal if $$\int_{-\infty}^{\infty}x(t)y^*(t)dt=0\tag{1}$$ From (1) it is clear that if two real-...
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  • 80.4k
3 votes

Iterative Kalman filters and system parameters estimation

Regarding the miss modeling, I am not sure how you can handle that because a good mathematical model is important inorder to get kalman filter getting to work. usually the more complex your model is, ...
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