Questions tagged [sampling]

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

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1answer
668 views

Relation between the DTFT and CTFT in sampling- sample period isn't as the impulse train period

I will quote an answer of Matt L. from this post (I didn't comment there because I can't) If you have a continuous-time signal $x(t)$, then the two signals you're talking about are $$\begin{...
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1answer
356 views

Why is one of the modulated frequency spikes smaller?

This is a simple amplitude modulation experiment. Both waves are sinusoids of the type cos(2 x pi x f x t). The base signal has a frequency 100Hz, and the ...
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1answer
110 views

Effect of nonlinear transformation on digital signal

Currently, I know that by passing a band-limited baseband digital signal through a nonlinear system results in the expansion of the original signal's bandwidth and creates harmonics. Therefore, I ...
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1answer
332 views

Denoising short, non-uniformly spaced, bandlmited sequences

Consider a bandlimited signal $x(t)$ with bandwidth $BW$. Samples of this signal are observed at non-uniformly spaced sample points in the presence of noise: $y(t_i)=x(t_i) + n_i \qquad i\in\{0,1,\...
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1answer
263 views

Interpolation formula for two dimensional signal reconstruction in the frequency domain from polar samples

In the book, Advanced Topics in Shannon Sampling and Interpolation Theory by Robert J. Marks II, one may find an interpolation formula for reconstructing a two dimensional signal from regular polar ...
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1answer
266 views

Impulse response of a continuous system sampled with zero-order hold

I've a continuous system $$F(s) = \frac{K}{Ts+1}.$$ I sample it with zero-order hold with sampling period $T_s$. The discrete system transfer function is $$ \begin{aligned} G(z) &= % \frac{z-1}{z}...
2
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1answer
123 views

Deciding on the FFT length for water waves in flume (wave facility)

Soon I'll be conducting experiments in a wave facility (flume) for my MSc thesis. And I would like to analyse wave spectra (amplitude and energy density). The time step (or 'accuracy') of the wave ...
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3answers
422 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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1answer
103 views

A Sampling theorem for power signals

Any function $f \in PW_{\pi}$ (where $PW_{\pi}$ is the Paley-Wiener space), can be expanded in terms of the orthonormal basis $\{e^{i n x}\}_{n\in \mathbb Z}$ as $$\hat{f}(x)=\sum_{n\in \mathbb Z}\...
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1answer
973 views

How to set sampling frequency of an acceleration data set

I have a set of accelerometer readings in $X, Y, Z$ axes obtained from an android based smart-phone. The data in $(X, Y, Z)$ was recorded at different time stamps and there is no uniform time period ...
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1answer
191 views

adequate sampling frequency in measuring acoustic emission

I am measuring acoustic emission signals. The a.e. frequency range is 20kHz to 1 MHz. The sampling frequency that I,set was 100kHz Samples per second. I must be ...
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2answers
646 views

Best Approach on How To Sample and Process

I'm looking for some advice, I am hoping one of the many forum experts could help me with some advice on the sampling and processing of signals. I am using an STM32F4 processor with 12 bit ADC and DSP ...
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1answer
4k views

Is digital up and down sampling linear/causal/time-invariant?

So I am trying to determine whether the process of up sampling (zero padding) and downsampling are linear, causal and/or time-invariant. Based on some resources I found online, I am under the ...
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1answer
91 views

Sampling distance

In paper: A. Vlad, A. Luca, and M. Frunzete, "Computational measurements of the transient time and of the sampling distance that enables statistical independence in the logistic map," in Proc. ...
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1answer
3k views

Relation between CTFT and DTFT

I need to transform this function: $$ x(t) = 4\sin(20\pi t ) - 5\cos(24\pi t ) + 3\sin(120\pi t ) $$ into a sequence $x(n)$ given that the sampling frequency should be 50 Hz. So that means the ...
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28 views

Showing that filtering a signal with bandwidth B with a brickwall filter of bandwidth W>B has no effect in time domain

The time-domain representation of $G(f) H(f)$, where $H(f)$ is an ideal brickwall filter of bandwidth $1/(2T)$ is: $$ \int g(\tau) \operatorname{sinc}\left(\frac{t-\tau}{T}\right) d\tau $$ I want to ...
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How should I sample the signal $f(t) = \sin(24t)^3\chi_{[0,0.52]}$ on the interval $[0,1.25]$?

I am from an applied math/PDE background and I don't usually deal with proper sampling and signal processing. I just take roughly what seems to be a good number of samples. But I would like to be ...
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133 views

Lagrange Vs Sinc interpolation

I was wondering what is the practical difference between Lagrange Interpolation using Farrow Structure and Sinc Interpolation? Both require pre-computation of time offset coefficients using a lookup ...
2
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1answer
68 views

How to describe correlated noise after the signal is oversampled?

The Gaussian noise in discrete signal models is usually assumed to be independent and identically distributed variables (i.i.d.). Does this mean that the signal must be sampled with the sampling rate ...
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0answers
61 views

Problem with 1st order PLL update equation

The output of a communication channel is given by: $x(t) = \sum_n{a_n}h(t-nT)$, where $\{a_n\}$ are BPSK symbols, $h(t)$ is the channel response, and $T$ is the symbol period. If there is an ...
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0answers
185 views

Intuitively, why is the comb function the sampling function?

The comb function can be used to sample a continuous signal. The comb function is defined as follows $$ C_T(t) = \sum_{k=-\infty}^{\infty} \delta(t - kT) $$ where $\delta$ is the Dirac function, ...
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1answer
519 views

Are resolution increase and noise reduction from oversampling mutually exclusive?

Oversampling a signal means sampling it with a significantly higher sampling frequency than the Nyquist rate. As far as I know, there are three advantages: Easier design of anti alias filter Increase ...
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132 views

How to Extrapolate a 1D Chirped Signal?

Following a past question, I'd like to extrapolate a signal like the one below: (red is signal, blue is the the extrapolated ) ...
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1answer
247 views

Determining sampling rate for signal reconstruction

I want to know how to determine the signal sampling rate required to reconstruct electrical signals whose frequency components are unknown, such as, for example, signals of charge/discharge voltage on ...
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64 views

How can I extract the 2 polyphase components of a signal after sampling at the half of sampling rate

Suppose I have a continuous signal $x(t)$, which was sampled using sampling function $s(t)$ whose sampling rate is $T_s$.How can I sample the continuous signal by Ts/2 instead of Ts in order to get ...
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46 views

Hardware selection for acquiring signal in digital form

I want to it clear that I am a mechanical engineer and so my knowledge on electronics and signal processing is limited. I am working in a hydrophone system. My job is to find the position of an ...
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0answers
81 views

Why does filtering the same discrete dataset while choosing different sampling rates yield different results?

If I have a two-dimensional discrete dataset (one space, one time), and I create subsets of this dataset by "sampling" (although the original dataset isn't continuous) it at different rates, should I ...
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1answer
559 views

Why is the magnitude of the second component of my FFT spectrum always the largest one?

While working with FFT, I have a strange case with a current experimental setup. I am working with beat frequencies (intermediate frequency output) and using a standard FFT algorithm (complex to ...
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0answers
664 views

Fast DSP with in-chip ADCs

I'm looking for a DSP, around 500MHz, with an in-chip ADC (preferably 2 but 1 will suffice) that samples around 20MSPS. Does any such DSP exist or do I have to use external ADCs?
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136 views

Upsampling Methods for Computed-Tomography

I have two sets of data of given Field of view, one of them only covers a subset of the FOV of the other. I therefore want to upsample the one with the larger FOV to combine it with the other one. So ...
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0answers
132 views

Instantaneous Frequency variation

I am looking for a method to calculate the instantaneous pitch variation within a speech signal for time-warping application. Sample by sample frequency variation knowledge within a frame will give ...
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0answers
120 views

Voice sample prediction scheme

I have some telephone voice audio with occasional "blips" in the audio. The blips appear to come from an IP link buried in the PSTN (this is a conceptual explanation, so don't worry about things like ...
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3answers
966 views

A question about the sampling theorem

Let's say I have a signal, containing frequencies up to $30$ kHZ. I am sampling this signal at $40$ kHz with infinite bit depth (just for theory). Will I be able to recover exactly all the ...
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6answers
1k views

Use of the Dirac delta as a sampling operator

As we are all taught in signal processing classes, the Dirac delta is not a normal function but a generalized function. It is sometimes defined as either the limit of some normal function whose ...
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3answers
474 views

Am I violating Nyquist?

I am using a DAC to transmit 2 different voltage levels. High and low. At 1Gsps. There is no carrier wave or anything. These are just raw 0 and 1 time samples going across a wire. On my ADC I am ...
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2answers
2k views

Quadrature modulation for FM and AM

This might be a naïve question, are these correct statements? Both amplitude and frequency modulated radio signals nowadays use quadrature modulation and demodulation as a mean to transfer and ...
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4answers
370 views

Sampling Theorem: How to know the value between two samples of a Signal

According to Sampling theorem, in order to reconstruct a signal we need to sample it at the rate => twice the highest frequency component of that signal. (provided signal is band limited). Let's say, ...
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2answers
961 views

Sampling frequency lower than half of sampled signal frequency?

In GNURADIO when RTL-SDR Source block is placed there is a parameter Sample Rate (sps) and ...
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3answers
5k views

sampling rate for band pass signal

The sampling frequency for band pass signal which is having frequency from 4 kHz to 6 kHz(rectangular shape from 4 to 6 kHz), can I prefer the sampling frequency of 12 kHz(2*the highest frequency ...
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2answers
218 views

What is meant by *sampling* in terms of the *sampling theorem*?

Let $y:\left(-\frac T2,\frac T2\right)\to\mathbb{C}$ be a square integrable function. The Fourier coefficients of $y$ are $$\underline{Y}(k):=\frac 1T\int_{-T/2}^{T/2}y(t)e^{-i\omega_kt}\;dt\;\;\;\...
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2answers
5k views

Reducing sampling rate by a non-integer factor

I have data that is sampled at 12 kHz. The downsample function in software such as MATLAB only allow you to downsample by an integer factor, i.e. from $12\to{6,4,3,...
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1answer
338 views

How do I convert a sampled complex signal to a real signal?

I’m writing a Soapy SDR plugin for the FL2K-SDR. Soapy SDR expects plugins to produce and consume IQ samples. However, the FL2K-SDR driver consumes only real samples. I know you can convert a real ...
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2answers
87 views

Ideal sampling using sinc funcion

Let $ x(t) $ be a bandwidth limited signal such as $ \forall |\omega|>\frac{\pi}{T} : X^F(\omega)=0 $ while $ X^F(\omega)$ is the signal's Fourier Transform. Let us denote $y[n]=\int_{-\infty}^{\...
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3answers
889 views

Precision measurement of sine wave amplitude with ADC

I want to measure amplitude of a sine wave input precisely with a limited resolution ADC. As an example suppose that I have $1\textrm{ MHz}$ pure sine wave input to the $320\textrm{ Msps}$ $10$-bit ...
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3answers
730 views

Applying Nyquist theorem to digital vs. analog audio quality

I had a recent conversation with a friend about analog vs. digital recordings. He shared his opinion that music recorded by analog techniques is of superior sound quality to music recorded by digital ...
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1answer
1k views

Different results applying DFT (formula only) and FFT on Matlab?

I have this function in time-domain and in frequency domain after fourier transform: $$s_1(t) = (t-2)e^{-t}u(t-2) $$ $$S_1(f)=\frac{e^{-2(1+j2\pi f)}}{(1+j2\pi f)^2} $$ First I create a time vector ...
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2answers
1k views

Offset effect in FFT magnitude

i will use matlab code just for convenience, i get the same behavior using a C++ code. I have two signals: ...
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2answers
565 views

Where can I find an authoritative (peer-reviewed or textbook) reference to sampling-induced beating?

I presume we are all here well aware about foldback aliasing when sampling signals above the Nyquist frequency; i.e. half the sampling rate. By contrast, the phenomenon of beating occurs when ...
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2answers
87 views

Types of interpolation used for reconstruction in DSP?

What are the different types of interpolation used in DSP for reconstruction of analog signal from discrete/digital signal I am able to somehow learn two types of interpolation 1st is "zero order ...
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2answers
66 views

How sampling aperiodic signal will result in periodic repetitions of the same

I am reading "Digital Signal Processing" - Proakis and often read that sampling guarantees periodicity (not exact as read) But I wonder how sampling aperiodic signal will result in periodic ...

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