Questions tagged [nyquist]

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LTI Filter for DAC Reconstruction

$\textbf{Question:}$ An analog-to-discrete is designed as, $$x[n] = x_a(nT)$$ In an attempt to recover the analog signal from its samples x[n], a D/A converter is designed as , where $x_1(t)$ is ...
1 vote
1 answer
371 views

Why does the bandwidth of a signal need to be half of the sampling rate? [duplicate]

Suppose I perform a DFT on some function with sampling rate of $\frac{1}{\Delta t}$. According to this page, the bandwidth, which is the maximum frequency that can be analyzed when performed the DFT, ...
5 votes
3 answers
647 views

Moving average before downsampling: effect on Nyquist frequency?

First the simple questions: Is there an effect on the Nyquist frequency when I apply a moving average filter on the raw data before I downsample? And what does this do to aliased frequencies? ...
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Discrete Fourier Transform of real valued input using half the amount of frequency bins

Quick question: Is it correct to define Discrete Fourier Transform like this, if my input signal is real valued: $$ X[k] = \sum_{n=0}^{N-1} x[n] \cdot e^{-i2 \pi n \frac{k}{N}} $$ Where $k \in \{0, 1, ...
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Nyquist frequency Plotting Distortions

I'm trying to plot some sinusoidal signals in Matlab. But while frequency is getting higher (closing to fs/2), results are getting distorted. I guess it's lack of my knowledge but distortion is ...
5 votes
2 answers
622 views

Is there a way to compute the spectrum effect of a non-linear function?

I'm interested in developing audio software. I've read the books by Will Pirkle and there's something I'm struggling to understand about how non-linear functions affect the frequency spectrum of a ...
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3 votes
2 answers
473 views

Filter amplifies frequencies at nyquist frequency. What's the purpose of such a filter?

I'm currently facing a filter that amplifies frequencies at the Nyquist frequency. The sampling frequency is $f_s = 10$ Mhz. What's a typical application for such a filter? This is how I generated ...
2 votes
1 answer
74 views

How does a CIC filter output meet Nyquist?

In this image from Understanding cascaded integrator-comb filters The bottom image shows the output response, with the entire range as passband: Even the CIC compensation filters are all passband to $...
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Is the slow waveform an alias - and why don't we see other alias'es of different frequencies?

The following figures are data from sampling the DC bus of an inverter for a BLDC/PMSM drive running a speed-loop with FOC. The upper subplots are FFT's of the signal and the lower subplots are of the ...
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Are there any recommended filter types for passband frequencies near Nyquist?

Is there a recommended filter type for frequency bands near the Nyquist frequency? I have been trying to design complex passband filter with passband $[0.8 ~~1]$ ( where $1$ corresponds to the ...
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2 votes
3 answers
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Why are real-world digital images not bandlimited?

In the materials about image resampling, it always mentions that real-world digital images not bandlimited. However no explanation is provided. For example, Sinc resampling in theory provides the ...
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1 answer
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Having Nyquist bin = aliasing?

Here I motivate the question by deriving FFT upsampling for $N \rightarrow 2N$ with even $N$. One might naively try xup = 2*ifft([xf[:N//2], zeros(N), xf[-N//2:]]), ...
4 votes
1 answer
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How is the maximum theoretical data rate of a channel equal to $2B\log_2(V)$ bits/sec.?

According to Andrew S. Tanenbaum (in "Computer Networks", Chap. 2, Section 4 "The Maximum Data Rate of a Channel"), the Nyquist/sampling theorem states that "if an arbitrary ...
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1 answer
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How to choose correctly oversampling ratio?

As many of us have noticed, last two months I am working on GMSK modulation and demodulation design. Before continuing my research, I want to be sure I chose the correct oversampling ratio ( how many ...
0 votes
1 answer
64 views

Reconstructing a signal from a Nyquist plot

I have a system which is like a blackbox which has just one input which could be a sinusoidal wave which is a sum of a range of frequencies, now the problem is that I dont have the time-domain output ...
1 vote
1 answer
76 views

What does the two following formulas mean?

I am a bit confused between the following two formulas: $$ f\le \frac{f_s}{2} \tag{1}$$ and: $$ f = \frac{f_s}{N} \tag{2}$$ Now I am given an ACF Plot of a sine/cosine wave and I am asked to find ...
3 votes
2 answers
363 views

How do we determine the required sampling rate of a closed loop control system?

Consider the controlled dynamical system $\dot{x}_t = f(x_t, u(t-\tau_{sd}))$, where $0<\tau_{sd}$ denotes the time delay caused by sampling. It is intuitively clear that the time delay caused by ...
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1 answer
76 views

What is the output signal's frequency when doing operations of two signals?

If I have two continuous time signals x(t) and y(t) of maximum frequencies Ω1, Ω2 respectively. I want to find the sampling frequency used used in continuous-discrete conversion of the following ...
1 vote
1 answer
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How do I determine the dominant frequency of a signal after sampling?

For example if I have a $10 Hz$ signal and I sample it at $19 Hz$ (less than the Nyquist frequency) how can I determine the dominant frequency of the output and why? If I then apply a lowpass filter, ...
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Sampling, filters, windowing, FFT. From theory to help on this coding list

My plan is to analyse the spectrum of samples from a microphone. I wonder how correct this suggestion is. The below description may then fail on several points. I am in need of somebody with a red ...
4 votes
3 answers
697 views

Stanford EE 261 HW6 Q1 - Sampling below Nyquist Rate

The problem (taken from here) asks for possible sampling rates that will not cause aliasing in the following frequency spectrum: The range of possible values after some math is given as $B_2 < f_s ...
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Given a signal that is not bandlimited, how do you properly take the FFT?

I assume that the Nyquist theorem doesn't apply, at least not in the standard sense, for a non-bandlimited signal. In my case, I sample the signal (in the time domain) above the Nyquist rate and then ...
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1 answer
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In what cases can you get aliasing below the Nyquist frequency?

I took the one-sided FFT of a signal and plotted up until the Nyquist frequency. Then, I took the real part of this FFT multiplied by $i\omega$ following a calculation that I'm trying to do of a ...
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1 answer
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Matching Filter & Raised Cosine Confusion

I'm reading from Communication Systems, 5th Edition by Simon Haykin. At some point we derived that Which is how the effect due to AWGN is minimized. Meanwhile, to minimize ISI we need $P(f)$ to be ...
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The raised cosine spectrum and Nyquist's criterion for zero ISI

For the past hour, I've been trying to understand what the book is trying to say here: This is Communication Systems, 5th Edition by Simon Haykin. We know that the Nyquist criterion is I'm unable to ...
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1 answer
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Inferring shape of information signal from its DFT?

I came across this question recently, and I am very confused by (b)(ii). b(i) gives $x_n$ = [0.5, 0, -0.5, 0]. My approach to (ii) was to recognise that $X_m$ represents the frequency content of the ...
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What is the symbol rate achieved with raised cosine filter?

The bandwidth of the raised cosine filter is w=0.5(1+r)Rs, where Rs is the symbol rate, and r is the roll-off factor. r=0 represents the Nyquist filter, for which Rs=2w. Any higher value for the roll-...
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Will or can a sampled signal with a limited sampling frequency have infinite bandwidth?

I know that a continuous-time digital signal with sharp edges (e.g. jumping from one y-Value to another discontinuously at the same x-value) will have infinite bandwidth. But what about sampled ...
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does T = 1/F always hold?

i just want to know if i use a sampling frequency of 100-110Hz and get a useful signal frequency of 50Hz (because of Nyquist–Shannon sampling theorem), is the period 1/50Hz or 1/100Hz? I've been told ...
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1 answer
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Sampling frequency vs Signal frequency

I've started recently working with the ADXL345 accelerometer with the goal of finding the velocity. And so far, I'm getting "okay" results after applying a second-order Butterworth filter to ...
-1 votes
1 answer
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Sampling with Rectangular Pulse and Nyquist Condition

The classical Nyquist theorem assumes that the sampled signal is obtained by multiplying the signal with dirac-delta functions separated by width 1/f_sample or less. Given such sampling we can ...
0 votes
2 answers
59 views

Aliasing in continous-time signal

I have the following signal and it was plotted with a sampling frequency (Fs) of 5Khz and F0 was then varied for 0.5Khz, 2Khz, 3Khz, and 4.5Khz. I obtained aliasing when F0 = 2Khz and 3Khz only. ...
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1 vote
1 answer
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Why is the bandwidth of each ZigBee channel in the 2.4GHz frequency band 2MHz, while the sampling interval of the ZigBee receiver is 0.5us? [duplicate]

From the Wikipedia, the XBee paper, the BlueBee paper, and the WeBee paper, I learned that: In the 2.4 GHz band, the bandwidth of each ZigBee channel is 2 MHz. For receiving a signal over one of ...
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ADC sampling of incoming signal and aliasing effect [duplicate]

I know from the sampling theorem, that the signal frequency $f_{sig}$ shouldn't exceed 0.5 of sampling frequency $f_{samp}$. I decided to have a look at it and tried for example $f_{samp} = 50 $ $kHz$ ...
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2 votes
2 answers
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Misunderstanding of Nyquist sampling theorem and minimum sampling rate

I sample my time-domain (TD) signal using a distance between time-samples of $\delta = (t_{max} - t_{min}) / N_t$, where $N_t$ is the number of samples taken. The sampling rate is $1 / \delta$. I have ...
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19 votes
3 answers
4k views

What sampling frequency should I use if Nyquist is not available?

I have the following homework question that confuses me: We have an audio emitter that can emit two signals: It either emits a sine wave at 23 kHz or it emits a sine wave at 25 kHz. The receiver has ...
-1 votes
1 answer
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The minimum frequency for signal modulation

I have a signal sampled with frequency 10 kHz. My spectrum is 1 kHz. As far as I went, according to the Nyquist theorem I can module the signal with max. 5 kHz (1/2 of sampling frequency). What's the ...
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Why are there copies of a signal in the frequency domain? [closed]

I only know about this from images and some videos and articles I've read, but I haven't managed to find an explanation. It only says they exist. This is what I mean: Blue is the frequency domain of ...
1 vote
1 answer
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Narrowest passband dsp filter one can apply

I was wondering how one would know the narrowest pass-band digital filter one can apply, given the original signal's sampling frequency. For example on a signal coming out from a 14 bit ADC acquiring ...
1 vote
5 answers
512 views

Why does twice the sampling rate (Nyquist Theorem) seem inadequate?

I was told in my electronics course that "to reproduce a wave, we need to sample it at least twice every period." If I take this to be literally true, then a sine wave with only 2-3 samples ...
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1 answer
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Which of the following sampling methods can be used to sample x(t) such that this signal can be uniquely recovered from its samples?

Assuming that a continuous-time $x(t)$ having its frequency content in the frequency band $1612\leq|F|\leq2015(Hz)$ is sampled with the sampling rate $Fs=806$ samples per second. Which of the ...
0 votes
3 answers
112 views

Why Matlab Spectrogram of slow and rarely sampled signal shows high frequencies

I have a signal, which was measured for 14.4 minutes (= 864 seconds). There are 192 measurements, so one measurement was done in every 4.5 seconds, which results in a 0.22 Hz sampling frequency if I ...
5 votes
2 answers
263 views

Nyquist frequency isn't working

The situation is that I have a signal with linearly increasing frequency, $$\text{sin}(2\pi\omega(t)t),$$ where $\omega(t)=a+bt$ for some $a$ and $b$, and we constantly sample at one point per second ...
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1 answer
194 views

Signal to noise ratio (SNR) of a CW signal

I understand the formula SNR = 6.02N+1.76 for a N-bit ADC which quantizes a modulated tone sampled at twice the BW. I am trying to understand what the same equation would be for a unmodulated CW tones ...
0 votes
1 answer
349 views

Dealing with normalized cut-off frequencies larger than 1.0

I am trying to create an FIR bandpass filter in python using scipy with the following characteristics: $$f_{c_{low}} = 310\,Hz$$ $$f_{c_{high}} =600\, Hz$$ giving me a bandwidth of: $$Bandwidth = f_{...
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1 vote
4 answers
353 views

DFT after the Nyquist limit

I usually do the DFT using the fft in Matlab. After the Nyquist frequency I don't see any result. Is it possible to perform a dft looking after the Nyquist frequency. I am asking this because I have ...
0 votes
1 answer
164 views

Optimal sampling frequency

I am working with microcontroller's ADC to sample the data. I know that Nyquist criteria tells us that the sampling frequency should be at least twice the highest frequency, but it might involve ...
2 votes
1 answer
534 views

Aliasing in Doppler Radar

my book about RADAR says that: If a Continuous wave radar sends a sine wave at frequency $f_T$ to a moving object (at speed V), a frequency $f_R$ is received. Their difference is called Doppler ...
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How to reconstruct original signal from sampled signal?

My original signal as f1=2; f2=5; fs=100; Ts=1/fs; t=0:Ts:1; xt=cos(2*pi*f1*t)+cos(2*pi*f2*t); figure plot(t,xt) as shown below figure. and my sampled signal ...
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Nyquist Frequency and Window Length

The Nyquist theorem states that the sampling rate must be twice the highest frequency to be observed. How does the length of the interval play into this relationship? The main resource that I found ...
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