Questions tagged [nyquist]

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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 ...
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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 ...
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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 ...
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3 votes
2 answers
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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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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 ...
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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 ...
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4 votes
3 answers
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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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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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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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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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3 answers
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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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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 ...
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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 ...
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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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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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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 ...
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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 ...
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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 ...
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1 vote
5 answers
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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 ...
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3 answers
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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 ...
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5 votes
2 answers
242 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
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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 ...
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1 answer
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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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4 answers
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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 ...
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1 answer
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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 ...
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2 votes
1 answer
308 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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2 answers
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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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2 answers
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Does the Shannon theorem not apply when the amplitude of a wave is changed faster than half the time period of the wave?

Shannon's version of the sampling theorem states that if a function contains frequencies all strictly less than $B$ hertz, then it is completely determined by giving its ordinates at a series of ...
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Selecting the Nyquist rate for a combination of signals

If several sine waves were combined but each had a separate frequency, for example 10 Hz, 20 Hz and and 30 Hz, what would the required Nyquist rate be for analysis? From my research, it suggests that ...
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2 answers
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How to deal with "weird" phase plots in bode diagram when designing a controller

I am trying to design a balance controller for a robot. With MATLAB simulink I arrived at the transfer function between the input and the pitch angle for the robot. I have plotted the bode and Nyquist ...
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Reconstruction of a signal based on non-uniform samples and a well below nyquist sampling rate

I have a set of non-uniform samples that are the following set of data over the course of 1 second: The rightmost column is in milliseconds, and the first three leftmost columns are each different ...
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10 votes
2 answers
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Does the Nyquist frequency of the cochlear nerve impose the fundamental limit on human hearing?

The bandwidth of human hearing by empirical data is $20 \; Hz$ to $20 \; kHz$. A cochlear implant stimulates the auditory or acoustic or Cochlear nerve directly so that the hearing can be improved in ...
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Wavetable and Nyquist: which size do I need?

I was reading this tutorial by the master earlevel, while trying to build some sort of wavetable. He says First, let’s back up and figure out how long our tables need to be. Recalling that we need to ...
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Restore real signal from its complex representation if sampled under Nyquist frequency

Assume we have: real signal: $s(t)$ its analytic representation: $s^+(t) = s(t) + j*H(t)$, where $H(t)$ - Hilbert transform of $s(t)$ Spectrum of $s^+(t)$ has only positive part, so may be sampled ...
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What should be IQ sample rate at least?

As i read, IQ sample doesn't need nyquist criteria. What is the mathematical representation of this result? Why IQ sample doesn't need nyquist frequency? I know that can be set to nyquist frequency ...
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1 vote
1 answer
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Aliasing below $f_s/2$

phi = exp(linspace(0, log(511), 1024)) - 1 x = cos(2 * pi * phi) Above will alias, despite peak instantaneous frequency evaluating to ...
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2 votes
1 answer
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A basic question regarding frequency analysis of an EEG signal

Assume that an EEG signal is sampled at $f_s = 300$ Hz then a 10000-point segment of it is selected, called $x[n]$. The corresponding 10000-point DFT is then computed and called $X[k]$. Assume further ...
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3 votes
1 answer
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Sampling pure tone sine waves [closed]

What would happen if I am using the maximum frequency as the sample rate for sampling a pure tone sine wave? For example, a $10\ \rm kHz$ sampling frequency for a $10\ \rm kHz$ monotone sine wave. ...
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1 vote
2 answers
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Confused on Pulse Filter Bandwidth and Symbol Rate Relation

***Still need help in 2021 - not fully clear still on Jan 20th *** I am confused about the relation between Sinc and Rectangle transform pair and how that relates the Bandwidth of Pulses, Bandwidth of ...
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Amplitude modulation vs sampling rate?

As a sampled tone's frequency nears $f_s / 2$, amplitude modulation grows apparent: ("Actual" curve in grey; blue is what we get if taking samples (dots) "at face value"). This is ...
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