Questions tagged [frequency-spectrum]

The frequency spectrum of a time-domain signal is a representation of that signal in the frequency domain.

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What does frequency domain denote in case of images?

I was just learning about the frequency domain in images. I can understand the frequency spectrum in case of waves. It denotes what frequencies are present in a wave. If we draw the frequency ...
Abid Rahman K's user avatar
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Why so many methods of computing PSD?

Welch's method has been my go-to algorithm for computing power spectral density (PSD) of evenly-sampled timeseries. I noticed that there are many other methods for computing PSD. For example, in ...
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"Complex sampling" can break Nyquist?

I have heard anecdotaly that sampling complex signals need not follow Nyquist sampling rates but can actually be gotten away with half Nyquist sampling rates. I am wondering if there is any truth to ...
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What is the difference between PSD and squared magnitude of frequency spectrum?

The power spectrum of a signal can be calculated by taking the magnitude squared of its Fourier transform. Being an audio person, the signal of interest for me would be a time series. How does this ...
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How to distinguish voice from snoring?

Background: I'm working on an iPhone application (alluded to in several other posts) that "listens to" snoring/breathing while one is asleep and determines if there are signs of sleep apnea (as a pre-...
Daniel R Hicks's user avatar
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Does using the Goertzel algorithm actually give better frequency resolution?

I am reading this article, and I am getting a little confused by the author's liberal use of 'frequency resolution' regarding the Goertzel Algorithm. Basic question: Does using the Goertzel algorithm ...
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How do you calculate spectral flatness from an FFT?

Ok, the spectral flatness (also called Wiener entropy) is defined as the ratio of the geometric mean of a spectrum to its arithmetic mean. Wikipedia and other references say the power spectrum. Isn'...
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Terminology: spectrum, spectrogram, spectrograph, sonogram, etc

In term of proper or accepted naming conventions of DSP graphics or instrumentation output, what is the difference between the words spectrum, spectrogram, spectrograph, and similar terms, and what ...
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Why does spectral leakage arise in an FFT?

I've tried googling and wikipedia-ing it, but I haven't gotten any answers beyond 'it's because the frequency of the input signal is sitting between two bins'. I understand that this is the reason, ...
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What image-processing techniques are ideal for this particular shift/scale invariant template matching?

A problem I had originally discussed in What methodology to use for discrimination of different (musical?) tones has evolved, and might have gotten a little simpler as I studied it in some more and ...
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Why do we use window in time domain rather than do FFT modify the spectrum and than inverse FFT

I thought that DSP would be done by using FFT of portions of a signal, modify the samples that result from FFT (since they represent the spectrum of our signal + noise) and remove any unwanted signals ...
quantum231's user avatar
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How can I plot frequency vs magnitude of wavelet transform?

I am running Morlet continuous wavelet transform. I have got wscalogram of signal and now I want to plot freq-magnitude like the following picture., but I don't ...
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How to make frequency axis for even and odd FFT length?

Can I get help on how to make frequency axis going from negative frequency to positive frequency, (in Hertz), that will be the x-axis in an FFT result, but given either an even length FFT, or odd ...
TheGrapeBeyond's user avatar
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When should I calculate PSD instead of plain FFT magnitude spectrum?

I have a thirty-second speech signal that was sampled at 44.1 kHz. Now, I would like to show what frequencies the speech has. However, I'm not sure what would be the best way to do that. It seems ...
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On using eigenvectors to estimate a signals' fundamental frequency, via MUSIC

Context: (Disclaimer: This is NOT a comm problem). I am trying to estimate the fundamental frequency of a real, periodic signal. This signal, was constructed by match filtering a raw signal, to that ...
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FFT frequency resolution

I'm having some problems understanding the FFT. Is the frequency resolution in the spectrum calculated as $\frac{\textrm{sampling rate}}{\textrm{number of FFT points}}$ or $\frac{\textrm{sampling ...
argh's user avatar
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Inverse polyphonic chord recognition

Polyphonic music transcription does not currently appear to be a solved problem. How about the inverse of a small portion of the problem. Are there any kind of spectral characteristics (from an STFT)...
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What is the bandwidth of a (real) sinusoidal tone, and pulse?

I would like to know how to go about calculating the bandwidth of: A constant (real) sinusoidal tone A (real) sinusoidal pulse. The question is as simple as that, but I am having a hard time with ...
Spacey's user avatar
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Why do I have frequency leakage in DFT after zero padding if frequency resolution is fine?

Let's consider this example: Fs=1000; Ns=500; t=0:1/Fs:(Ns-1)*1/Fs; f1=10; f2=400; x=5+5*sin(2*pi*f1*t)+2*sin(2*pi*f2*t); X=fft(x); In this scenario, frequency ...
user3616359's user avatar
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What is spectral entropy?

Can anyone explain what spectral entropy is? Does noise with a restricted bandwidth have the same spectral entropy as white noise?
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Recognizing math functions within songs

I'm new to DSP, and just discovered this StackExchange, so apologies if this isn't the right place to post this question. Is there a resource that describes genres in a more mathematical terms? For ...
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Which transform most closely mimics the human auditory system?

The Fourier transform is commonly used for frequency analysis of sounds. However, it has some disadvantages when it comes to analyzing the human perception of sound. For example, its frequency bins ...
user76284's user avatar
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3 answers
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What is spectral whitening?

What is meant by "spectral whitening" in DSP? What effect does spectral whitening have when used in image processing? (visually or otherwise...) Where might spectral whitening be useful in audio ...
hotpaw2's user avatar
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A DFT “periodic inputs” question

Why do people say that the fast Fourier transform (FFT) “views”, or “interprets”, or “assumes” its input sequence is periodic? I ask this question because the activities of viewing, interpreting, and ...
Richard Lyons's user avatar
12 votes
4 answers
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DFT - Removing window effect in spectral domain with convolution

I was thinking about the DFT windowing subject and a thought came to my mind. A DFT will yield the spectrum of a signal convoluted with spectrum of the window used, therefore having a main lobes and ...
Pier-Yves Lessard's user avatar
11 votes
3 answers
22k views

Why are sidebands generated in AM and FM?

When the signal is modulated onto the carrier in the electromagnetic spectrum, that signal occupies the small portion of the spectrum surrounding the carrier frequency. It also cause sidebands to be ...
Sufiyan Ghori's user avatar
11 votes
3 answers
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What is meant by "spectral moment"?

I have consulted the almighty oracles of google and wiki, but I cannot seem to find a definition for the phrase "the moment of the spectrum". A legacy work text I am reading uses it in the following ...
Spacey's user avatar
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Creating a spectrogram

I've been trying to work out the logic for this task, and plan to use the KissFFT source package to perform the fast fourier transform. Please let me know if this looks about right: Allocate an FFT ...
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Harmonic Product Spectrum limitations in pitch detection

I've made a pitch detection algorithm using HPS and I'm facing a problem. I'm a beginner with signal processing and this site helped me before, so I though I should ask. For higher pitches ( ...
Rad'Val's user avatar
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2 answers
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On the de-noising of time-frequency images

I am wondering what techniques might be available for 'de-noising' the following example time-frequency image that was created using Welch's method. The following plot was created from a robotic ...
Spacey's user avatar
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How to perform a Rubberband-Correction on spectroscopic data?

I basicaly understood how the Rubberband/Baseline-correction works. The given spectrum is divided into (N) ranges. The lowest points in every range are determined. The initial baseline is built out ...
チーズパン's user avatar
10 votes
2 answers
2k views

Is spectral leakage due to windowing 'different' for the DTFT and DFT?

I'm currently trying to improve my foundational understanding of spectral leakage due to windowing. The more I have been reading about it, the more I'm starting to think that 'windowing spectral ...
Izzo's user avatar
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2 answers
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Phase shift and phase spectrum terms in multidimensional signal

I know about phase of a 1D signal. But when I go into higher dimensions like 2D,3D etc, it becomes headache to grasp the concept. What are the terms phase shift and phase spectrum mean in case of ...
devraj's user avatar
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What transform can I use to "zoom" in a specific portion of a signal's spectrum?

If I recall correctly, there is a variation of the DFT that can be used to analyze a specific band of the spectrum of a signal. How is it called?
Arrigo's user avatar
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How do you handle negative frequencies in the power spectrum of a complex signal?

When we apply the DFT operation on a real signal $x[n]$ to get $X[k]$, then take the square magnitude of the $X[k]$, $\lvert X[k]\rvert^2$, the power spectrum is symmetrical. You can take the ...
Mike's user avatar
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1 answer
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Designing a feature vector for discriminating between different sonic waveforms

Consider the 4 following waveform signals: ...
Andy's user avatar
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9 votes
4 answers
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When is it true that "the Fourier transform of the autocorrelation is the spectral density"?

I am currently struggling on the book "System Identification: Theory for the User" by Lenart Ljung (freely available here) about the definition of the spectrum (around page 33). As I have ...
NokiYola's user avatar
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3 answers
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Why calculate negative frequencies of DFT?

This answer says that when calculating the DFT on a real valued signal, the (roughly) second half of the bins are the complex conjugates of the first half of the bins. Firstly I was curious if that is ...
Alan Wolfe's user avatar
9 votes
5 answers
3k views

Does windowing affect Parseval's theorem?

I have computed Fourier transform from ecg data.It does obey Parseval's theorem, relation $$\sum_{n=0}^{N-1} \Big| x[n] \Big|^2 = \frac{1}{N} \sum_{k=0}^{N-1} \Big| X[k] \Big|^2$$ is fulfiled. ...
wiedzminYo's user avatar
9 votes
2 answers
24k views

Why images need to be padded before filtering in frequency domain

In image processing books , we are told that Images need to be padded while doing filtering in the frequency domain. Why we need that zero padding ?
Prashant Singh's user avatar
9 votes
3 answers
32k views

Number of DFT (FFT) Points Required for a Specific Frequency Resolution for an Oversampled Signal

I have a bandpass signal centered at 2 MHz and bandwidth of 50 kHz (the signal frequency varies from 2 MHz - 25 kHz to 2 MHz + 25 kHz). This signal is being sampled at 10 MHz. I want a frequency ...
Vinod's user avatar
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9 votes
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Frequency resolution and timestep in DFT

I am learning DFT and I am not sure I understand it correctly. I am just going to write out the process of DFT and I am asking you to tell me if I am thinking the right way. Suppose we have a signal ...
c0dehunter's user avatar
9 votes
1 answer
7k views

Large spike at the center frequency when using Ettus X310

I am using the Ettus X310 SDR and GNU radio. On the GNU radio schema I have a standard UHD USRP source block connected to a GUI FFT sink - basically I'm just displaying the spectrum of the raw signal ...
Tihomir Meščić's user avatar
9 votes
3 answers
22k views

Frequency resolution of DFT

I know that the frequency resolution in a DFT is given by sampling rate upon the total number of samples. $$\Delta f = \frac{f_s}{N}$$ But, what I want to know is where does this relation comes from? ...
Rhinocerotidae's user avatar
9 votes
1 answer
6k views

Scalogram (and related nomenclatures) for DWT?

My understanding of the scalogram is that, for a particular row, the scores of the projection of the input signal with the wavelet at a particular displacement is shown. Across rows, the same thing ...
Spacey's user avatar
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9 votes
2 answers
25k views

How to shift the frequency spectrum?

Lets say we have a spectrum ranging from -X MHz to +X MHz. I would need to correct the frequency error in the spectrum by shifting the zero component to the middle (0 Hz). If the output (the ...
user1166780's user avatar
9 votes
2 answers
5k views

Spectrum of FSK signal

I have implemented a simple V.23-like FSK modem in C here. The peculiarity of the chosen modulation is such that 0's and 1's are sent as tones of two different frequencies (2100 Hz and 1300 Hz ...
Alexey Frunze's user avatar
8 votes
4 answers
857 views

Estimating period of low frequency oscillations: autocorrelation vs. Frequency approaches

I have a noisy signal around $15\text{s}$ long sampled a $32\,\text{Hz}$. I am trying to estimate the peak frequency or period for a low frequency component with expected frequency in between $0.08\,\...
00__00__00's user avatar
8 votes
5 answers
33k views

Difference between DC component and zero frequency component of signal

We know that Fourier Transform of a signal exists if it is absolutely integrable and it exists for periodic signals if impulse functions are allowed. If we consider the fourier transform of $\text{...
spectre's user avatar
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8 votes
3 answers
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Common methods of transmitting digital data through an extremely noisy audio signal?

I am developing software for transmitting data from a computer to a mobile device using audio. Specifically, from the computer's speaker to the device's microphone. (I am developing both the sender ...
Keith's user avatar
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