# Questions tagged [nyquist]

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### Computing shifted signal without first reconstructing

Looking for a solution to the following problem: A signal $x(t)$ is band limited to $B$ Hz, and sampled above the Nyquist rate, with corresponding $f_s = 1/T$. If the sampled signal is given by ...
3k views

### Explanation of binning in frequency analysis post-FFT

I am creating an Android app which records sound for t seconds at a sampling rate of 44.1kHz with a buffer size of 8192 (16 bit mono samples). I need to plot a ...
120 views

### Is it possible to lose half the samples, and yet see the full spectrogram as the original signal?

Consider an speech audio signal sampled at 16,000 samples per second. Plot its spctrogram. If we delete every other sample from input signal, we get y[n] = x[2n] for all n. It seems that if we plot ...
442 views

### Compensation for Irregular Time Step for DFT (FFT)

I want to run a clustering algorithm (svm, knn) on the ferquency spectrum data of a temperature sensor that published at irregular times. Here is the temperature data to take the FFT: I got the ...
560 views

### Nyquist frequency and DC

Im studying the DSP book by Steven W. Smith. On page 41 he covers the Nyquist frequency. He makes up an example by writing the following. ... consider an analog signal composed of frequencies ...
758 views

### why Sampling with higher than nyquist frequency is causing aliasing?

fm=20000 and I am sampling following signal at 65000 Hz: ...
183 views

### Can I ignore the Nyquist criterion?

If I have a signal with frequencies up to 2000 Hz but I'm only interested in the frequency range up to 500 Hz, is it correct to sample at 1000 Hz $(f_\mathrm s \geq 2 \cdot f_\mathrm{max})$? Or do I ...
2k views

### How to determine Nyquist Rate

I have the Fourier Transform of a signal. How can I determine the Nyquist Rate of that signal? What is the formula for that?
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### What is the relationship between frequency vector and the peak frequency in FFT?

I am fairly new to both Matlab and FFT. I would like someone to explain to me the relationship between the frequency of the wave being processed, the number of point (usually called NFFT), the Nyquist ...
59 views

### What exactly is captured in a Sample of the Nyquist-Theorem variety?

I'm new to DSP and was thinking of sampling in the traditional music creation way, in that you capture a sound and play it back, warp it, etc., but when I thought about the Nyquist theorem, I realized ...
830 views

### Minimum Channel Bandwidth for PCM

Please check if my answer to GATE IN 2010 question 11.20 is correct/can be improved upon. So, every $\frac{1}{f_s}$ sec, a sample is taken. The signal amplitude is quantized into $2^n$ levels such ...
50 views

### Discrepancy in stability conditions when calculating via RH criterion and Nyquist criteria

I have the following open loop transfer function for a unity feedback system. $$G(s)=\frac{K(s+20)^2}{s^3}$$ 1.When using RH criterion it can be easily proved that the closed loop transfer function ...
761 views

### Minimum possible sampling frequency for continuous time signal

A continuous-time signal $x(t)$ has the magnitude spectrum $\lvert X(F)\rvert$ shown in Figure 6. The signal is sampled to obtain $x(n)$ using the sampling frequency $F_s$. Determine the minimum ...
517 views

### Why doesn't the sampling theorem work in this case?

In this example, under "Discussion", we can see that the Nyquist sample rate will result in samples with the value zero only. But why is this? I thought the sampling theorem said that if you sample ...
796 views

### What is the minimum sampling duration to capture a given frequency?

Due to the Nyquist rate, you need to sample twice as fast as the highest frequency you want to measure. Then when you do a FFT the number of samples determines the number of bins and thus the ...
1k views

### The Nyquist-Theorm behind the fft

I saw a code in Python in the scipy.org (http://docs.scipy.org/doc/scipy-dev/reference/tutorial/fftpack.html) and found this: First question: Is it right that T = 1/800 <==> fs = 800 Hz fulfill ...
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### Calculate Max Number Of Harmonics for given Sample Rate?

How do I calculate the maximum number of harmonics a complex wave can have based on the sample rate? Say I Have a 20hz fundamental and a sampling rate of 44100 hz. My instinct is to take 44100/2 = ...
33 views

### Sampling a signal with varying frequency

Question I'm trying to figure out the sampling rate for my ADC to sample essentially signal essentially of the form: $$y(t) = \sin(\max(t, \omega_{max})\times t) + n$$ where $n$ is noise. Context ...
445 views

### Nyquist Maximum data rate formula for PCM

The Nyquist maximum data rate formula for a binary PCM is given by $$C = 2B\log_2L$$ I'm not very sure what "$B$" is here. Is it the bandwidth of the signal being sampled or is it the channel ...
61 views

### Calculate aliasing of $x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$ when sampled with $F_s = 1000$

I'm asked to sample the signal $$x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$$ with sampling frequency $F_s = 1000$ and plot the magnitude spectrum for the resulting sampled signal. My thinking is ...
100 views

### Nyquist sampling

I know that if $f_\mathrm{m}$ is the "Nyquist frequency" (max frequency) and $f_\mathrm{s}$ sampling rate then $f_\mathrm{s}>2f_\mathrm{m}$. Am I correct so far? I have a signal $x(t)$ with max ...
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### Do Nyquist samples have the same sum as the integral of the signal?

Assume I sample a signal according to the Nyquist criterion. Then I perform a simple summation / integral over a linearly interpolated signal. Is this equivalent to the integral over the continuous ...
49 views

### Nyquist Rate (Sampling Frequency) for ${f}^{2} \left( x, y \right)$

We are given that $f(x,y)$ is highest frequency is $\omega$ what will be the frequency sample rate if we want to restore the function of the form $g(x,y)=f^2(x,y)$ Would it be correct to say that ...
96 views

### Distortion of a signal consisting of two periodic components

We have a signal $$x(t)=U_1\cos\omega_1t+U_2\cos\omega_2t$$ whose frequencies are $f_1=100\,\text{Hz}$ and $f_2=600\,\text{Hz}$. This signal is being discretisated in time using unipolar ...
64 views

### Sampling below Nyqust Frequency

My understanding of Nyquist's theorem is that you need to sample at a rate that's twice the bandwidth of a signal to fully recover it. What exactly does the bandwidth mean in this context and what ...
263 views

### Invertibility of Room Impulse Response: Reproducing Research Paper

I have been trying to reproduce this paper¹. Few things which are unclear to me. The paper talks about finding whether a given Room Impulse Response(RIR) is invertible or not based on Nyquist plot. ...
189 views

### Lock-In Amplifier Sampling Rate

For a digital lock-in amplifier (synchronous demodulator) I have a sinusoidal reference signal in the range of 10-15kHz, the amplitude and phase I want to observe changes very slowly <10Hz. My ...
I have a signal $x(t)$ for which I want to find the Nyquist frequency : $$x(t) = \frac{\sin{\pi t/2}}{\pi t/2} \ast \sum^\infty_{n=-\infty}\delta(t-10n)$$ I am trying to solve this in the time ...