Questions tagged [complex]

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Doubts and some confusion on variance for complex rv

This question is in continuation of the one asked here. Let's say that the measurement noise $w$ or any random variable is circularly Gaussian complex. If the imaginary and real components each has ...
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1answer
106 views

Destructive interference on the Autocorrelation of the time signal of periodic CPFSK-signals.

An FSK-signal with a frequency-shift $\Delta F$, a symbol-stream $x$, $x(n) \in {\{-1,1}\} $ and symbol duration $T$ has the complex envelope: $$f[x](t)=\exp\left(2 \pi i \Delta F T \left(\sum_{l=0}^{...
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2answers
751 views

DFT of a complex sinusoid

I'm attending this course (Coursera: Audio Signal Processing for Music Applications) in which the professor derives a general equation for Discrete Fourier Transform (DFT) for a complex sinusoid. The ...
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1answer
1k views

Autocorrelation and Power Spectral Density (Discrete)

The Autocorrelation, $\phi_{aa}[\kappa]$, of a discrete time random process, $a[k]$, is defined as: $$ \phi_{aa}[\kappa] = \mathrm{E}\left\{ a[k+\kappa]a^*[k] \right\} $$ Taking its fourier ...
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1answer
666 views

Use of complex numbers to calculate Doppler effect?

First of all, I'm a beginner in this field, please tell me if any of what I'm asking is too basic / can be found with some google research. I have a situation with a static TX and a moving RX (v is ...
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1answer
589 views

Frequency spectrum of complex equivalent Baseband Signal - Frequency Content around carrier frequency

Basically my objective is to generate a complex equivalent baseband signal of an AM modulated wave in MATLAB. Then to view the difference in frequency spectrum of AM modulated RF signal vs complex ...
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4answers
3k views

On the meaning of s-plane and it's link to a transfer function

Considering Fourier analysis and let's say I'm walking on the blue frequency axis in the below 3D plot from zero towards infinity: So each time I encounter a non zero blue bar, I check the frequency ...
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1answer
888 views

Confusion regarding pdf of circularly symmetric complex gaussian rv

Considering a random variable $x$ that takes in values from a complex domain. Its real and imaginary components are totally uncorrelated. I am following this link and also studying this document. In ...
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1answer
3k views

What would be the variance for complex number?

When $x$ is a zero mean random variable then $$\sum_{n=1}^N x_n x_n^T = N \sigma^2_x\,\text,$$ where the variance is $\sigma^2_x$. I'm considering Complex Normal Distributions where the real and ...
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2answers
4k views

FFTs of a complex signal - separating the real and imaginary parts

I have a complex time varying signal at a single frequency x = a + jb where a represents the contribution from the cosine basis ...
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2answers
6k views

Considering the FFT of Real & Complex Signals

I've been implementing a website to perform the FFT of various signals, real & complex. Examining the first example, a real signal $x[n] = 10 cos(2\pi\times4n)$, I got the following FFT: Which ...
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2answers
3k views

Bandwidth with complex sampling

On the transmit side, I have a 20 MHz carrier frequency carrying a signal with bandwidth of 40 MHz (so 0 Hz to 40 MHz, center at 20 MHz). On the receive side, I have a dual channel ADC with each ...
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3answers
471 views

How should this fft output be intepreted?

I am currently reading some code, so I can understand how this FFT output is actually been stored. I have a function which computes FFT of audio file, and stores is in the format. ...
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1answer
86 views

Is the calculation of variance correct from an estimator — confusion regarding complex number where I am going wrong?

I have an expression for the varaince of measurement noise obtained from an estimator. The measurement noise is additive white gaussian having values in complex domain. I have squared the term $(.)^2$,...
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1answer
329 views

MATLAB's $\tt filter()$ function for complex valued data [closed]

I want to use the filter() function to implement an FIR filter having complex data values as the input to it. For real, I used this function as ...
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1answer
257 views

Covariance matrix $P$ and $Q$ for complex valued data

The equations for the Kalman filtering are IM = H*X; IS = (R + H*P*H'); K = P*H'/IS; X = X + K * (y-IM); P = P - K*IS*K'; The covariance matrix in my ...
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1answer
3k views

Matlab: What is the proper way to calculate mean square error for complex numbers

I am confused regarding the calculation of mean square error involving complex numbers. Considering, the true channel coefficients to be ...
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5answers
2k views

Equation for impulse train as sum of complex exponentials

Could someone please break down what's going on in this equation for me? I understand what the left side looks like, but not so much how the right side is the same thing. Impulse train: $$\sum_{m=-\...
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3answers
647 views

Compression algorithms specific to complex signals

I am looking for (lossy or lossless) compression algorithms dedicated to complex signals. The latter could be composite data (like the left and right for stereo audio), a Fourier transformation, an ...
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3answers
1k views

How do you save/convert an image to be in the frequency domain?

Quick Note: I don't believe this is a subjective question... however if it is I will gladly modify to be more objective In ImageJ, if I take the FFT of an image, how can I save this new frequency ...
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3answers
563 views

Discontinuity in the angle of a complex exponential signal

Plotting this complex expontential: $$z[n]=100e^{j0.1n},\quad\text{we have a discontinuity at}\quad \arg[n]=10\pi$$ I guess this is related to the angle formula: $$\theta=\arctan\left(\frac{\Im\{z[...
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3answers
3k views

FIR filter design for complex signal

I have a complex signal generated by an impedance analyzer. What is the best approach for designing a low pass FIR filter for this? Is a real filter applied separately to the real and imaginary ...
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5answers
2k views

Does it make sense to have complex numbers representing real-world audio signals?

In this course (Coursera: Audio Signal Processing for Music Applications) the professor uses an example of obtaining the DFT of a complex sinusoid: \begin{align} x_2[n]&=e^{\jmath\left(2\pi f_0 n+...
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1answer
87 views

Is it possible to Denormalize a matrix of complex numbers?

In this article, FFT and I-FFT are achieved as the following: FFT steps process starts with a Bitmap image. Bitmap-image to Integer-image Integer-image to Complex-image Apply Forward-FFT to Complex-...
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1answer
1k views

How to perform an FFT on a signal with a sampling rate of 44100?

This is probably a very simple Signal Processing question but I can't quite work it out. I'm currently writing an android app which needs to perform an fft on audio data taken from the phone's ...
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1answer
541 views

Smoothing complex data by convolution

I need to smooth noisy complex data with a Gaussian filter. Right now, I apply the filter to real and imaginary part of the data separately, which needs two convolutions. The intended results are the ...
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1answer
70 views

Difference equation with complex zero

Let's assume I have the following transfer function: $$ H(z)=\frac{z-\left(\frac{1}{\sqrt{2}}+i \cdot \frac{1}{\sqrt{2}}\right)}{z} $$ It looks like a first order highpass-filter with a complex zero ...
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3answers
2k views

Where and how do an Image and a complex number meet?

I am trying to implement a Gabor Filter bank. Gabor Filter uses a complex function. How do the filters like Gabor Filter operate on an Image? Does a complex number represent an entire Image or only ...
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1answer
642 views

Filtering/Analyzing Complex Data stream

I receive complex I and Q data from an USRP. I want to do a Hamming window LP filter on the data. However, I don't get the grasp of how I use the complex data. It is unusual because most of the time ...