Questions tagged [signal-analysis]

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How to convert raw pulse sensor data into actual pulse?

I've built a simple device, which sends readings from a pulse sensor to a PC. I get these data: What technique or algorithm can I use in order to calculate the pulse rate (beats per minute) from ...
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0answers
59 views

Intuition of Location on the Conic Axis TDOA solution

In an old paper "A New Approach to Geometry of Range Difference Location", there is a mathematical derivation that does not include any mention of the relationship to the underlying problem. In the ...
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4answers
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What does the exponential term in the Fourier transform mean?

We know that Fourier transform $F(\omega)$ of function $f(t)$ is summation from $-\infty$ to $+\infty$ product of $f(t)$ and $e^{-j \omega t}$: $$ F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ e^...
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2answers
143 views

Accessing Maximum Value from a Singular Value Decomposed Matrix

I have read few image enhancement papers, where an image is enhanced in transformed domain using either DCT (discrete cosine transform) or DWT (discrete wavelet transform) with SVD (singular value ...
2
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3answers
427 views

Can use of Fourier transform be minimized completely with the help of Laplace and Z transform?

Fourier transform has different types like continuous Fourier transform (CFT), Discrete time Fourier transform (DTFT) and Discrete Fourier transform ( DFT). CFT can be used in case of continuous ...
2
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3answers
545 views

Computer exercises and solutions in signal processing

I am very interested in this question and can literally not find anywhere a simple answer, so apologize in advance if it does not fit well this community. I am looking for either an online resource ...
2
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3answers
4k views

Fundamental frequency

Can someone help me: I have a signal which consist of three frequencies; for example, $f_1=800\,\text{Hz}$, $f_2=1050\,\text{Hz}$, $f_3=1600\,\text{Hz}$. How can i compute the fundamental frequency? ...
2
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4answers
2k views

Why does the frequency in the DFT have to be an integer?

I don't know why the result of DFT and FFT in MATLAB like below images.. fs=128; t=0:1/fs:1-1/fs; x=cos(2*pi*3.5*t); X=fft(x); N=length(x); n=0:N-1; f=fs*n/N; plot(f,abs(X)/N); If I set the ...
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2answers
6k views

What is the practical meaning of the variance, covariance, mean value?

What is the practical meaning of variance, covariance and mean for a signal?
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2answers
2k views

Can the order of filtering and downsampling be exchanged?

Say for example, I have a signal with maximum frequency at 600Hz, and I originally oversampled it at 2000Hz. Afterwards I was only interested in frequency less than 500Hz. I guess I could first filter ...
2
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4answers
16k views

Measure the SNR of a signal in the frequency domain?

How do you measure the SNR of a sinewave in the frequency domain? (Assuming no filtering.) Suppose: $$x(n) = s(n) + n(n)$$ Create the signal (nCycles of a sinewave) in MATLAB...: ...
2
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1answer
115 views

Why a pair of complex-conjugate zeros provide a nulling filter? (FIR filter case)

FIR filter having a pair of complex-conjugate zeros that lie on the unit circle, with zeros of the form: $$ z_1 = e^{j\omega_i}\qquad\text{and}\qquad z_2 = e^{-j\omega_i} $$ And transfer function: $$ ...
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3answers
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“Fourier Transform can localize signals in frequency domain, but not in time domain.” — What does it mean in layman's terms?

I was studying the introduction to wavelets and its benefit over the frequency domain. I said that: Fourier analysis can't localize signals both in time and frequency domain. Fourier analysis can ...
2
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1answer
4k views

Time-frequency representation of sound signal using Matlab

I am currently doing a project on sound signal processing by using MATLAB. I have a problem regarding creating the command line so that I can get a graph containing frequency by its time. But this ...
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6answers
41k views

Simplest way to implement FIR filter in C/C++

What's the simplest way to implement a FIR filter in C/C++ ? (I don't want to have to use a third-party software like Matlab or Octave in order to compute the coefficiens because I have to use ...
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5answers
2k views

Difference Between Dirac delta and unit impulse function

The definition of Dirac delta function states that it gives a value of $\infty$ at t=0 and 0 elsewhere. But, the definition of unit impulse function states that it gives a value of 1 at t=0 and 0 ...
2
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3answers
229 views

Detect valleys of a signal

I have raw values that are coming directly from a sensor (on the fly). These values are coming from a wearable sensor installed on a cows neck. When the cow ruminates (meaning that it chews food that ...
2
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1answer
413 views

A very basic question about processing high frequency signals

A standard frequency for a modern computer processor is 1-3 GHz. The frequency of a GPS signal is ~1.5 GHz. My question is how is it possible for a computer to do anything at all with a signal that it ...
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2answers
2k views

How to quantify asymmetry of a signal?

I'm looking for a suitable measure in order to quantify the asymmetry of a signal. I've read this: Detect signals degree of imbalance and this: How to measure the agreement between to curves? but I ...
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2answers
1k views

How do I perform the sifting process in empirical mode decomposition?

I am programming a voice activity detection algorithm and I found a paper that recommends the use of HHT. I have been trying to program it and understand how to calculate $m1(x)$, but the shifting ...
2
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1answer
8k views

Use Butterworth and Chebychev filters

I need to calculate frequency response, phase response and apply to signals the Butterworth, Chebychev1 and Chebychev2 band-pass filters. I'm developing in C++ with Qt, and I'm looking for algorithms ...
2
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2answers
55 views

Dominant Frequency Peak Decreases with Increasing Window Size

I have a signal that looks like this. I analyse it using fast Fourier transforms to identify the frequency with the largest peak, which is always close to zero. (There are no other clear peaks.) If I ...
2
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2answers
562 views

Periodicity of sum of discrete signals

In my lecture slides for school and from this website here "The sum $z[n] = x[n] + y[n]$ of periodic signals $x[n]$ with fundamental period $N1$, and $y[n]$ with fundamental period $N2$ is periodic ...
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2answers
10k views

How do I find the fundamental period of the given signal?

I am having a problem in finding the fundamental period of the signal $x(t)$ given below: \begin{align} x(t) &= 2\cos\left(\frac 45 \pi t\right)\sin^2\left(\frac{16}{3} t\right)\\ &= 2\cos\...
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3answers
121 views

Weighted Sum of Auto Correlation - Lower Bound

Given a vector $ v $ with elements $ {\left\{ {v}_{n} \right\}}_{n = - \infty}^{\infty} $ and denoting $ {v}_{n}^{\left( k \right)} = {v}_{n - k} $, namely, a shifted vector by $ k $ elements (Mind ...
2
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1answer
93 views

Beginner's book in signal processing with practical examples on fault detection in electrical motors

I'm an electrical engineering graduate and I'm working on condition monitoring for electrical motors and generators. My goal is to improve reliability of electric rotary machines in such way, that any ...
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2answers
103 views

Mathematically speaking, is a “signal” a function or the set of outputs from a function

In engineering it is well known that we abuse the notation of a function $f: A \to B$ with the image of that function $f(t) = \left\{y \in B\mid f(t) = y, t \in A\right\}$ When we say: let $f(t) = \...
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1answer
978 views

GPS signal acquisition

I have a set of GPS satellite signal data, the set is 1 ms long and has the information of two satellites (satellite number, code phase and frequency) buried in noise. This data has a carrier ...
2
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1answer
139 views

adjust mean of signal using exponential

I have discrete signals whose values are between 0 and 1. I wish to post-process such a signal such that the mean of its values equals 0.5, yet keeping maximum and minimum values 0/1 intact. ...
2
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4answers
4k views

Estimate frequency and peak value of a signal's fundamental

How can I find out frequency and peak value of a signal's fundamental? Please do consider the following: The peak value of some harmonics might be higher than that one of the fundamental The ...
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1answer
550 views

Very first values of y[n] in an IIR filter

I use a simple biquad IIR filter : ...
2
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2answers
149 views

Autocorrelation and Spectrum Density

Wiener–Khinchin theorem states that autocorrelation function and power spectral density are a Fourier-transform pair - see Wikipidia (and lots of other resources). That means autocorrelation should be ...
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4answers
94 views

Extracting fundamental amplitude/phase from only half a period of a pseudo-sinusoïd

Before you read my problem, I've summed up my experiments in a notebook available here. So, I have a few noisy samples (~50) of a pseudo sinusoidal signal for which I use a traditional discret ...
2
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1answer
133 views

Impulse response of a transfer function

Lets say we have a transfer function from an LTI-system that goes as follows, and we want the impulse response for it: $$\frac{10\cdot e^{\left(-\mathrm{i}\right)\cdot \pi\cdot f\cdot 8}}{5+\mathrm{i}\...
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3answers
67 views

Is there a problem with using the WAV format for non-audio signals?

I have biological signals sampled at 1 kHz. The signals tend to behave fairly simply, sinusoidally. The software I've used to collect these data uses their proprietary format (*.adicht) and so I have ...
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1answer
122 views

$\lim \limits_{a \to 0} \frac{1}{a}[u(\frac{t}{a}+\frac{1}{2})-u(\frac{t}{a}-\frac{1}{2})]= \delta(t) $

It would be very helpful if someone could provide the intuitive reasoning and mathematical proof for: $$F_a(t):=\frac{1}{a}\left[u\left(\frac{t}{a}+\frac{1}{2}\right)-u\left(\frac{t}{a}-\frac{1}{2}\...
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2answers
197 views

How to perform downconversion using a DSP

I read that to perform downconversion, first, I need to generate a sine wave with the same phase and frequency as the transmitter's and then multiply the signal received by the generated sine wave. I ...
2
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1answer
185 views

Definition of energy of a signal

I was wondering why the energy of a signal is defined as $$E=\int_{-\infty}^{\infty}|x(t)|^2dt$$ I mean, I know that it is a definition, but is there a physical reason for it being defined like that?...
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3answers
4k views

Type of filter, given difference equation?

Given a difference equation, how do we tell if it is an IIR filter or FIR filter? For example, y(n) = x(n-3)+y(n-1) . Is it FIR or IIR? Can you please give me a way to figure this out? Thanks! :)
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3answers
242 views

Separating a signal into its constituent components

First off, I apologize for possibly incorrect use of jargon, as I am new in this area. I have a type of signal that I am assuming can be described by an arbitrary number (let's say $n$) of basis ...
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1answer
1k views

Estimating Filtered Noise Variance

Assuming I have samples of a colored noise. I know the empirical Variance of those samples. I also know the bandwidth of the filter which colorized the noise (Only the bandwidth, not the actual filter)...
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1answer
5k views

Determine the optimum receiver and the corresponding $P_{eM}$ for an AWGN channel

I have a source that emits $M$ equiprobable messages, which are assigned signals $s_1, \dots,s_M,$ that are equidistant by $a$. That is, if we plot the $s_k$ signals in a horizontal axis they are dots ...
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5answers
702 views

Interpreting the amplitude of signals in fourier transform

I totally understand the concept of fourier transform, but one thing thats bothering me is the amplitude that we plot in the frequency domain. What does that amplitude of each frequency signifies? Is ...
2
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1answer
38 views

Sample & Hold: Estimate jitter delay of an ADC

I've got a question regarding the effects of sample and hold. My input signal is $x$, and my output signal $x_{SH}$. The error between the signals is $e_{SH} = x_{SH}-x$. The sampling frequency is ...
2
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1answer
35 views

Filtered signal does not follow my cut off frequency

I filtered my signal with low pass filter butterworth forth order with cutoff frequency of 50 hz. However when I compare the filtered signal with original one in frequency domain, it seems that the ...
2
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1answer
89 views

Is there any way that we can perform speech recognition without using Fourier transforms?

I am trying to research about speech recognition and why everyone uses Fourier transforms in going about the topic. I know that we get information related to the frequency of each sound uttered which ...
2
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1answer
241 views

What is discrete angular frequency?

I am currently reading a paper about speech enhancement. The paper uses Spectral Subtraction Method. On that section, The paper stated that ω is the "discrete angular frequency index of the frames" ...
2
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2answers
257 views

how is this method of proving shift invariance correct

I got this answer from here. But i don't know how this method is correct. Until now to prove shift invariance what i did was : step 1: delay output and write it in terms of input. step 2: delay input ...
2
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2answers
310 views

Isolate High Variance vs Low Variance Sections of Signals

I have the following one-dimensional signals: The goal is to identify the sections with smaller variances compared to the rest (For Python, that is to get their index value in the array). In the ...
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2answers
301 views

Measuring vibrato rate of a sung note

I'm doing a project where I need to measure the rate of vibrato cycles in a sung note under various conditions. The stimulus will be a several-second-long audio sample of a held a capella note with ...

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