28 votes
Accepted

Does the Nyquist frequency of the cochlear nerve impose the fundamental limit on human hearing?

Does the Nyquist frequency of the Cochlear nerve impose the fundamental limit on human hearing? No. A quick run-through the human auditory system: The outer ear (pinnae, ear canal), spatially "...
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21 votes

A question about sampling rate of cosine signal

It is actually not distorted, it is sampled at high enough rate. What fools you is the straight lines drawn between sample points, it gives you a false impression of the waveform. It shows you a ...
  • 1,471
15 votes

What is the difference between phase noise and frequency noise?

Phase Noise and Frequency Noise are not two different noise sources, they are artifacts of the same noise, it is just a matter of what units you want to use. Frequency and Phase are directly related ...
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12 votes

What is the maximum possible frequency of human voice/speech(That can be generated through human vocal cords)?

The fundamental speaking frequency of humans can reach up to around 1kHz, although higher values than, say, 500Hz usually appear only while singing. The harmonics and non-tonal parts of speech can ...
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12 votes

What is the maximum possible frequency of human voice/speech(That can be generated through human vocal cords)?

Especially What is the maximum value of frequency that human speech can have? This depends on how exactly you define it. Fricatives ("s","f","sh" ...) and plosives (&...
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10 votes
Accepted

Amplitude modulation vs sampling rate?

The OP's opening statement is incorrect: $f_s > f_{max}/2$ prevents frequency aliasing for a bandlimited signal, but not amplitude aliasing $f_s > 2 f_{max}$ prevents aliasing. It's as simple ...
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9 votes

Doppler shift in time domain?

The term Doppler Shift is actually a bit of a misnomer. The frequencies are not actually shifted but they are scaled (see http://fourier.eng.hmc.edu/e101/lectures/handout3/node2.html for definition of ...
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9 votes

A question about sampling rate of cosine signal

The actual requirement is to sample at GREATER then twice the bandwidth, not at a rate equal to it... So only your 80Hz same set actually meets the requirement, because the 60Hz case is ambiguous in ...
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8 votes

Estimation of Amplitude, Frequency and Phase of Linear Combination of Harmonic Signal Beyond the Leakage Resolution of DFT

Solving the Linear Combination of Real Harmonic Signal The data model is given by: $$ x \left( t \right) = \sum_{i = 1}^{M} {a}_{i} \sin \left( 2 \pi {f}_{i} t + {\phi}_{i} \right) + n \left( t \right)...
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7 votes

Designing High Pass Filter to Remove DC Offset from a Signal

If the DFT is the Uniform sampling from $ 0 $ to $ 2 \pi $ then the first bin is given by: $$ x[k] = \sum_{n = 0}^{N - 1} x[n] $$ Namely it is the sum of all the samples. Hence in order to remove ...
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7 votes

How to Normalize Frequency in MATLAB

The interval resolution should be determined according to data you want to analyze. It is equivalent to the question, what magnification of your Micro Scope would you use? Well, it depends on the ...
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7 votes
Accepted

Simple and efficient algorithm to detect frequency and phase of a sine signal

Note: I originally posted this answer for the Stack Overflow copy of this question, before realizing that it had also been asked here. It somewhat duplicates pichenettes' answer, but I felt it still ...
7 votes

Are there libraries for extraction of sound wave features?

From the ones I've been using I can recommend: YAAFE - very pleasant to work with in Python ESSENTIA - another one I like particularly due to Python integration aubio FEAPI Aquila - friend of mine ...
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7 votes

Frequency Analysis (DFT / FFT) of a Signal Without a Constant Sampling Frequency (Non Uniform Sampling in Time Domain)

The DFT Matrix for Non Uniform Time Samples Series Problem Statement We have a signal $ x \left( t \right) $ defined on the interval $ \left[ {T}_{1}, {T}_{2} \right] $. Assume we have $ N $ samples ...
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7 votes
Accepted

Understanding the $\mathcal Z$-transform

Consider a liner discrete-time system. Assume we can define it in terms of an input-output relation as follows (you can assume a more general model but it is enough for our purpose): $$a_0y[n]+a_{1}y[...
  • 4,115
7 votes
Accepted

Meaning of a null coefficient at 0 Hz

A zero coefficient at DC simply means the mean of the waveform is 0; bin 0 of the DFT is identical to calculating the mean value scaled by $N$. Consider the general expression for the DFT: $$X(k) = \...
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7 votes

Is there other basis possible for DFT?

$k/N$ with $N$ bases is the only basis which is all of: Orthogonal & invertible. Means we don't lose any information. Invertibility can be seen to follow from the DFT being a square (N x N) ...
6 votes

Fundamental frequency

A signal which is the sum of sinusoids with different frequencies $f_i$ is only periodic if $$f_i=k_if_0,\quad i=1,2,\ldots$$ is satisfied for some $f_0$ and integer values $k_i$. Or, in other words,...
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6 votes
Accepted

Am i performing Sinesweep correctly?

The theory behind sweep-sine measurements of LTI systems requires a signal with constantly changing the frequency. You cannot simply playback few tones - the whole frequency range is necessary. So ...
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6 votes

Frequency Shifting in MATLAB

Try to remember what happens when you multiply a signal with a cosine function with a frequency of Fc. Namely, what's the shifting operator in Frequency domain? ...
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6 votes
Accepted

How to Flip Spectrum Around DC?

The article Handling Spectral Inversion in Baseband Processing that you refer to in your question is not about simple inversion of the frequency axis, but it is about inversion of the frequency axis ...
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6 votes
Accepted

Frequency of a DFT Bin

If you have a signal of 9 samples, namely $ {\left\{ {x}_{n} \right\}}_{n = 0}^{8} $ its DFT is given by $ {\left\{ {X}_{k} \right\}}_{k = 0}^{8} $ Now if the sampling rate is $ {F}_{s} $ the bin ...
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6 votes

Audio frequency modulation algorithm

You need to build a time varying delay, where you can modulate the delay amount over time. The peak delay modulation is a function of your maximum desired frequency shift and the modulation ...
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6 votes

A very basic question about processing high frequency signals

In digital signal processing, one almost never deals directly with high-frequency signals. The reason is that the frequency band that a signal occupies is completely irrelevant to the information that ...
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6 votes

Discrete Time Signal Property

I think it means the "apparent" frequency of oscillation. It's poorly worded. What's happening is that the frequency is increased to the Nyquist rate in the first half and then above it, causing ...
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6 votes
Accepted

Discrete Time Signal Property

Take a complex exponential $$x[n]=e^{jn\omega}\tag{1}$$ Let's assume that $\omega=\pi$. This gives $$x[n]=e^{jn\pi}=(-1)^n\tag{2}$$ (because $e^{j\pi}=-1$). Eq. $(2)$ shows that a signal with ...
  • 80.9k
6 votes
Accepted

Why is it called continuous-time frequency?

$\Omega$ is the usual angular frequency in radians per second, and is equal to $2 \pi f$. It is the way to measure frequency for continuous-time signals. In discrete-time, frequency is measured in ...
  • 4,751
6 votes

What Is the Bilateral Filter Category: LPF, HPF, BPF or BSF?

Bilateral Filter is indeed an Edge Preserving Filter. Moreover, due to being Spatially Variant Non Linear Filter it can not be applied using Fourier Transform. Since it has no representation in the ...
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6 votes

A question about sampling rate of cosine signal

There is no aliasing as 𝑓 = 30 Hz is less than or equal to the folding frequency, 30 Hz and 40 Hz, respectively. Yes and no. There isn't significant aliasing when you're sampling at 80Hz, because ...
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5 votes
Accepted

Calculating values of frequency bins in Python

This is simply how Discrete Fourier Transform (i.e. Fourier Transform theory applied on sampled signal) works. You get an output of length N if your input has ...
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