41 votes
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The difference between convolution and cross-correlation from a signal-analysis point of view

In signal processing, two problems are common: What is the output of this filter when its input is $x(t)$? The answer is given by $x(t)\ast h(t)$, where $h(t)$ is a signal called the "impulse ...
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32 votes
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Stationary vs non-stationary signals?

There is no stationary signal. Stationary and non-stationary are characterisations of the process that generated the signal. A signal is an observation. A recording of something that has happened. A ...
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31 votes
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What are advantages of having higher sampling rate of a signal?

Sampling at a higher frequency will give you more effective number of bits (ENOB), up to the limits of the spurious free dynamic range of the Analog to Digital Converter (ADC) you are using (as well ...
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22 votes

Difference between discrete time fourier transform and discrete fourier transform

alright, i'm gonna answer this with an argument that "opponents" to my rigid nazi-like position regarding the DFT have. first of all, my rigid, nazi-like position: the DFT and Discrete ...
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21 votes
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Difference between discrete time fourier transform and discrete fourier transform

The discrete-time Fourier transform (DTFT) is the (conventional) Fourier transform of a discrete-time signal. Its output is continous in frequency and periodic. Example: to find the spectrum of the ...
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21 votes
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Why doesn't sampling a periodic continuous-time signal yield a periodic discrete-time signal?

If the ratio between your sampling frequency and the frequency of your signal is irrational, you will not have a periodic discrete signal. Assuming you have a 1-kHz sine wave and you sample at 3000*...
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21 votes
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Why do we need DFT when we already have DTFT/DTFS?

The answer is the same to the question: "Why do we need computers to process data when we have paper and pencil?" DTFT as well as the continuous-time Fourier Transform is a theoretical tool ...
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19 votes
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What kind of filter is that? Is it IIR?

This is the FIR filter, although it looks like an IIR. If you calculate the coefficients you get finite impulse response: $h=[1]$ This happens due to zero-pole cancellation: $Y(z)-0.5Y(z)z^{-1}=X(z)...
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19 votes

The difference between convolution and cross-correlation from a signal-analysis point of view

The two terms convolution and cross-correlation are implemented in a very similar way in DSP. Which one you use depends on the application. If you are performing a linear, time-invariant filtering ...
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  • 22.9k
19 votes

Stationary vs non-stationary signals?

@A_A's good answer misses one point: stationarity or nonstationarity are generally only applied to stochastic signals, not deterministic signals. In general, when statistical tests are applied for ...
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18 votes

What kind of filter is that? Is it IIR?

Jojek's answer is of course correct. I would just like to add some more information because much too often have I seen the terms "IIR" and "recursive" confused. The following implications always hold: ...
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17 votes

Difference between Digital signal and Discrete signal

Suppose you have a continuous time analog signal. It is continuous in both time and amplitude. Now when you sample it ,you get discrete samples every Ts seconds. Now you have discrete samples(discrete ...
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16 votes
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DSP or signal/image/data processing jokes

An airplane is leaving Warsaw (the capital of Poland), and gets caught in a terrible winter storm. The plane rolls, pitches and yaws. The crew is expecting the plane to crash or break up at any time. ...
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15 votes

Why Does the DFT Assume the Transformed Signal Is Periodic?

There are already some good answers, but I still feel like adding yet another explanation, because I consider this topic extremely important for the understanding of many aspects of digital signal ...
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14 votes

What Kind of Features Can I Extract from a Signal

Some Features: Mean. Variance. Skewness. Kurtosis. Dominant 3 frequencies in the DFT. Energy of the 3 dominant frequencies. Max Value. Min Value. Median. Total Variation. Usually I'd compute them in ...
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14 votes
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What should be the correct scaling for PSD calculation using $\tt fft$

There is only one correct way of scaling DFT when calculating PSD with RMS values. Given input signal $x$ and its DFT $X$, the exact formula is: $$\mathrm{PSD}=\frac{2\cdot \hat{X}}{f_s\cdot S} $$ ...
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13 votes

How to learn MUSIC algorithm?

Read the original paper: Schmidt, R. O. "Multiple Emitter Location and Signal Parameter Estimation." IEEE Transactions on Antennas and Propagation. Vol. AP-34, March, 1986, pp. 276–280 You may also ...
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  • 1,071
13 votes
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Shift a signal by fraction of a sample

There's a good overview article which appeared in 1996 in the IEEE Signal Processing Magazine: Splitting the unit delay: tools for fractional delay filter design. The nice thing about it is that there'...
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13 votes
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Zero Padding of FFT

It's true that zero-padding in the time domain corresponds to interpolation in the frequency domain. If you have a length $N$ signal $x[n]$, its discrete Fourier transform (DFT) is given by $$X[k]=\...
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13 votes
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What is the difference between natural response and zero input response?

First it's important to realize that many authors use the terms zero-input response and natural response as synonyms. This convention is used in the corresponding wikipedia article, and for instance ...
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13 votes

Why do we need DFT when we already have DTFT/DTFS?

TL, DR: world pervasive algorithms (FFT-related)! The continuous Fourier transform, the Discrete-time Fourier transform (DTFT) and the Discrete Fourier transform (DFT) share conceptually similar ...
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12 votes

Does it make sense to have complex numbers representing real-world audio signals?

So it seems like real-world (discrete) audio signal might have complex values when being represented digitally, No, you misunderstood that. The discrete audio time signal doesn't have non-real ...
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12 votes

Are there any real world applications for complex-valued signals or impulse responses?

Absolutely! Conjugates are mentioned in textbooks because conjugation has no effect on real signals, but it does on complex ones. This way, formulations are more general and apply to both real and ...
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11 votes

Why Does the DFT Assume the Transformed Signal Is Periodic?

It comes from the definition of the time domain signal: $$ x \left[ n \right] = \sum_{k = 0}^{N - 1} X \left[ k \right] {e}^{\frac{2 \pi i n k}{N}} $$ You can see by definition that $ x \left[ n \...
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  • 41.3k
11 votes
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Power of a Discrete time signal

The power of a discrete-time signal $x[n]$ is given by $$P_x=\lim_{N\rightarrow\infty}\frac{1}{2N+1}\sum_{n=-N}^{N}|x[n]|^2$$ which is identical to the first formula in your question. The second ...
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11 votes

How do I explain a complex exponential intuitively?

From a graphical point-of view, it is an infinite spring, whose distance between adjacent coils reflects the frequency of the complex exponential: If you have a 1D time x-axis, you may be used to ...
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11 votes

Digital filter coefficients from low-pass to high-pass

You can apply a so-called all-pass transformation to a discrete-time low-pass prototype filter in order to convert it to other standard filters (such as high-pass, band-pass, and band-stop). This is ...
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11 votes
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This is how my professor is finding the frequency response of an LTI system when given the impulse response. Is this wrong?

Your professor is right, and you're almost right too. The filter is clearly an FIR filter, but because its frequency response can be expressed as a geometric series, a recursive implementation is ...
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  • 80.4k
11 votes

A case that zero padding increase real resolution and extract more info than naive DFT?

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10 votes

DSP or signal/image/data processing jokes

In high school math class I finally got the courage up to ask the cute and brainy girl at the front row out on a date. She just looked at me with a discouraging face and as she waved her hand face ...
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