In signal processing, sampling is the reduction of a continuous signal to a discrete signal.

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Why do we use discrete-time sampling?

I have been reading Signals and Systems (2nd ed.) recently. Chapter 7 is about sampling. Oppenheim uses discrete-time signals and continuous-time signals to explain sampling. But why do we need ...
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28 views

Undersampling and Phase Light Curve

I have an under sampled data set of a binary star with a 4 hour period. Its been sampled several times per week (yes per week) for 10 years. The resulting data is folded in a Phase diagram, using a ...
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63 views

What should be the correct scaling for PSD calculation using $\tt fft$

I would to calculate the PSD of a signal using FFT however the result do not match with periodogram command. What did was as follow : ...
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1answer
61 views

Finding the fundamental frequency from Autocorrelated data

I'm writing an app in which I need to find the fundamental frequency of a note produced by a trombone. To do this I'm taking the FFT of audio data from a microphone and then using autocorrelation code ...
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27 views

Upsampling and comb function

Could somebody explain how upsampling works with comb function. How comb function looks for upsampling process? (if it possible I would appreciate if answer would be related to DFT)
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55 views

Sampling the impulse response

Given two IIR filters (one Low-Pass and one High-Pass) designed using Butterworth, how can I know if they can be obtained using sampling the impulse response?
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96 views

Making a low pass filter for irregular samples

We are interested in reconstructing the red channel of a scene. The red channel is slowly varying. Unfortunately the camera does not have a Bayer sensor, and the red samples are irregularly spaced ...
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58 views

Time Domain Example of Nyquist/Shannon?

I looked at an old thread, Nyquist Frequency Phase Shift, but was left wondering still about oversampling. I learned Shannon 40 years ago, then worked 30 years in (s/w) engineering, but now retired I ...
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24 views

Sampling theory and frequency spacing

If a CT signal $x(t)$ is sampled for one ($1$) second and $4096$ samples are generated: Isn't the highest frequency that can be sampled without aliasing ($4096/2$) $2048\textrm{ Hz}$? If a $4096$...
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52 views

How to perform an FFT on a signal with a sampling rate of 44100?

This is probably a very simple Signal Processing question but I can't quite work it out. I'm currently writing an android app which needs to perform an fft on audio data taken from the phone's ...
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1answer
52 views

Define comb function in terms of exponential function

I have one signal with $N$ samples and I want to downsample it by factor of $M$. Essentially my downsampler is comb function which takes every M$^{th}$ sample while others are set to zero, i.e., $$ \...
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66 views

Aliasing after downsampling

Let me start with time domain representation of the original signal \begin{equation} x_n=\sum_{k=0}^{2N-1}X_ke^{j\frac{2\pi nk}{2N}} \end{equation} where $2N$ is number of time/frequency samples ...
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51 views

Philosophy of perfect inter-sample interpolation

How would you define perfect (inter-sample) interpolation, and is it possible? To quote Armifinn's prior answer: "I guess the most important result is that for signals with bandwidth limitation, ...
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28 views

Comb function and downsampling [duplicate]

I understand role of Dirac comb function in downsampling in theory but I have problem with showing it mathematically. Let me start with time domain representation of the $2N$ periodic original signal ...
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2answers
68 views

Mathematical justification for zero padding?

This question asks what's the point of zero padding. The accepted answer is certainly very insightful, but I don't understand a big chunk of it: Zero padding allows one to use a longer FFT, which ...
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1answer
28 views

What is the link between equation of a continuous signal versus equation of its sampled form?

I have just started DSP self-learning. I am a little confused by this 'end of the chapter' exercise question from Chapter 2 of "Understanding Digital signal processing" 3rd edition by Richard G. Lyons....
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44 views

Elegant way of calculating minimal sampling frequency without aliasing for annoying signals

Given a symmetric Fourier transform with finite support as below, there's an algorithmic procedure to determine the minimal frequency for sampling without aliasing: Find an integer $L>1$ ...
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1answer
29 views

LTI system input upsampling

Let's assume that a linear and time-invariant system is sampled at 2 different frequencies $F_{s}$ and $2F_{s}$ (e.g. 5Hz and 10 Hz). It gives $$Y_{F_{s}}(z) = H_{F_{s}}(z)X_{F_{s}}(z)$$ $$Y_{2F_{s}}(...
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76 views

Given a continuous time signal, does the minimum Nyquist sampling rate depend on the choice of the set of basis functions?

This is my first question on a StackExchange. When the basis functions to represent a signal are chosen as $e^{j\omega t}$ such as in a continuous-time Fourier transform then the sample rate $f_\...
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10 views

DWT initialization from nonuniform samples

Let $D\subset\mathbb R$ be compact, let $f:\mathbb R\to\mathbb R$ be a contintinuous function with support $D$. Let $\phi(x)$ be a well-defined scaling function, in the sense that it generates a ...
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50 views

Sampling rate versus number of sample of I and Q

I am acquiring data of an O-QPSK signal (chip rate : 2Mchip/s) with a SDR. I am undersampling the signal at 20 Mhz (carrier is at 2.8 GHz) so I respect the Shannon-Nyquist criterion that you need to ...
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29 views

Artifacts in sub-sample delay

There are at least two ways of achieving sub-sample delay. One is to simply over-sample the signal and then delay it by the wanted sub-sample amount. The over-sampling is equivalent to creating new ...
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29 views

Improve $\rm dB$ level after upsampling audio

I am doing upsampling from $44.1\textrm{ kHz}$ to $48\textrm{ kHz}$ on android device, using $\rm sinc$ interpolation. The output $\rm dB$ level is upto the mark for wave file up to $15\textrm{ kHz}$....
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41 views

Gaussian Pyramid - How is Subsampling Rate Related to Sigma?

I found a gaussian pyramid implementation in a MOPS paper (feature detection). They use sampling rate $s=2$ and $\sigma=1$ - i.e. to generate a new level of the pyramid, the current level is smoothed ...
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37 views

Upsampling and zero order hold

Maybe to someone this question may seem quite easy but I have a problem grasping it. Namely, assume that we have two systems A and B with sampling rates $f_A$ and $f_B$ where $f_A>f_B$ and $R=\frac{...
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52 views

Digital Filters deal only with samples, right?

I'm new to digital filters. So I'm trying to get things right and I can't find an explicit answer to my question on the internet. Question: Digital filters only accept samples as input? I mean the ...
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1answer
38 views

MATLAB and sampling rate

I have a question about sammpling rate in MATLAB. I read a .wav file using audioread(). It give me sampled data called ...
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2answers
51 views

Aliasing Square Wave

I'm having a really weird issue with generating waveforms from frequencies C1 to C8. When I generate sine waves, everything sounds good; no problems whatsoever. However, when I generate a square ...
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1answer
36 views

OFDM demodulation, how to set the sampling rate?

I have a signal for which I know the OFDM burst length (from the autocorrelation function of the signal) T_burst and the FFT size 1024 (by measuring the channel ...
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2answers
53 views

Sampling rate vs sampling time of FFT

I am having some trouble understanding the sampling time and frequency used in the computing of the FFT, and I was wondering if someone could make it clear for me : The Sampling time: the time in ...
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1answer
49 views

Envelop detection with low sample rate?

I have a signal up to $3\textrm{ MHz}$. The ADC that sample it has a rate of $1.5\mu s$. So a full $T$ of the signal is $0.3\mu s$, and I can only sample each $1.5\mu s$. It sounds not enough, but I ...
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48 views

Flat top sampling to a step shape signal

Flat Top Sampling During transmission, noise is introduced at top of the transmission pulse which can be easily removed if the pulse is in the form of flat top. Here, the top of the samples are flat ...
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40 views

Should the order of a filter be proportional to the sampling rate?

I have designed a fir filter with my desired frequency response at a specific sampling rate and filter order. If I were to redesign my filter for a new higher sampling rate, should I change the filter ...
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43 views

Output a sine wave from samples-limits?

Using a micro-processor of 48MHz, I am trying to output a sine wave from the DAC (digital to analog ), and I am not sure if my ...
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55 views

Generating very short signals

So I need to program (using Java) some things that include generated sounds. I am struggling to understand how to make it work because I require a rather short signal while still using a sampling rate ...
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44 views

Sampling frequency of audio

Based on what we choose sampling frequency when sampling some song? Do we use Nyquist–Shannon sampling theorem, or maximum sampling frequencies are pre-defined, so it will never come to aliasing ...
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50 views

Sampling a sinusoidal signal

Consider the signal $g(t) = \cos(2\pi\lambda t + \phi)$ that is sampled with a frequency $\tau$. Let $g_k$ denote the values of $g$ at the times $t_k =\frac{k}{\tau}$, $k \in \mathbb{N}$. (a) Show ...
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93 views

Random sampling vs uniform sampling

In this paper of Lustig, he speaks about a something which appears unintuitive: sampling at random may exhibit better performance than sampling uniformly. I tried to understand this starting from page ...
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29 views

Simple sample and reconstruction code - MATLAB

I am trying to go from theory to code. I take x (let say 16KHz is continuous time) then I sample it in 2Khz So I do ...
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1answer
22 views

EEG signal processing with sampling frequency

What is the relation between sampling frequency and the frequency of the signal after sampling? For example sampling frequency is 100 Hz, that is the signal contain maximum frequency of 50 Hz. Then ...
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1answer
35 views

how to sample and modulate a gps gold code

I am trying to simulate the data transmission of a GPS satellite. Telecommunications is not my field so I am struggling a bit with some concepts. I managed to generate the Gold code of the GPS ...
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66 views

Sampling Rate and SNR

Assume I have a signal that oscillates between 10KHz and 9Khz every 500msec (Change happens linearly, so at t=0, it is 10KHz and it goes to 9.5Kz at t=250msec and 9KHz at t=500msec and frequency start ...
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51 views

How to do the highest resolution FFT?

I wish to do the FFT of streaming audio data coming into a computer. I am just interested in frequencies from 80 Hz up to 1000 Hz but with a frequency resolution of 3 to 4 Hz and no more. Basically ...
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61 views

Why is $e^{i2\pi Nf_snT}=1$?

Why is $e^{i2\pi Nf_snT}=1$ in snippet from book?
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3answers
78 views

Performing DFT of streaming audio problem. Is there a limit?

I am trying to write software that will perform the discrete fourier transform of real time data coming from the microphone into the sound card on a computer. I am using Java with the javax.sound APIs....
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2answers
114 views

Aquila DSP C++ Library - Wave file FFT analog frequency off by factor of 4?

I'm working with the Aquila C++ DSP library. I'm computing the FFT of a wave file (16 bit depth, single channel, 44100 sample rate). I am using a window size of 16384 to calculate the FFT spectrum. I'...
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3answers
110 views

What is the underlying concept behind Bandpass sampling?

Can you suggest me some books/webpages on Bandpass sampling? I undestand that if the signal is restricted between $f_L$ and $f_H$, then the minimum bandwidth required is $2(f_H - f_L)$. But say the ...
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51 views

Closed-form expression for Whittaker-Shannon interpolation for non-bandlimited signals

For a bandlimited signal $x(t)$ that is reconstructed after Nyquist-sampling at intervals $T$, $$x(t) = \sum_{k=-\infty}^{\infty} {x[k]\textrm{sinc}\left(\frac{t-kT}{T}\right)}$$ where $x[k]$ = $x(...
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2answers
38 views

How do we actually obtain samples to form discrete time samples? [closed]

I'm in my second week of an online DSP class and I'm still kinda lost on some of the concepts of what we are actually doing. I'm hoping you guys can help clear up my understanding. Please forgive me ...
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31 views

Approximation of Step Response from Data with delay

How can I approximate a Step Response curve from a measured data of a single input and a single output using Matlab while the delay between the input and the output is 30 minutes?