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Questions tagged [complex]

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0
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3answers
39 views

In case of Complex DFT spectrum, why the x axis range from N/2 to N point mean a negative frequency?

When we transform a complex signal into frequency signal by using a complex DFT, The range from N/2 to N point on the X axis of the spectrum mean a negative frequency... But i cant understand why ...
6
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2answers
92 views

For complex values, why use complex conjugate in convolution?

Taken from Adaptive Filter Theory (2014) written by Haykin page 110 : $$y(n) = \sum_{k=0}^{\infty} w_k^*u(n-k), \quad n=0,1,2,...$$ where $u$ and $w$ are complex values. My question is why use ...
-1
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4answers
91 views

What are real-valued and complex signals and why is the Fourier transform of a real-valued signal Hermitian?

I have confusions in these concepts: What are real-valued signals? What is the difference between it and complex signals? Why is it so that for real-valued signals, the spectrum of negative ...
0
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2answers
61 views

Why complex signal has no imaginary spectrum

I am learning about complex sampling. I am confused why $~e^{ j 2\pi f~ n}~$ has only a real spectrum. I would have thought the $j ~\sin(2 \pi f n)$ would produce a single spike in imaginary spectrum ...
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0answers
21 views

Using complex number in non-negative matrix factorization (NMF) for signal source separation

In short, I wonder which kind of spectrum can be modeled using complex number in NMF. And could an imaginary part possibly be a vector? For detail, inspired by audio processing paper that used ...
1
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2answers
50 views

Convolution of real with complex signal

Let $x[n]$ be real signal and $y[n]=\exp(j3\pi n)$ be a complex signal Would the convolution between those two signals be $$x[n] * \Re(y[n]) + jx[n]*\Im(y[n])$$?
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0answers
22 views

Removing outlier data points from frequency-domain signal

Hello signal processing stack exchange, I have a complex frequency-domain signal representing the impulse response of a physical system over some range of frequency space. As an artifact of the ...
1
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1answer
69 views

Is there a technical term for the sum I + Q

Most likely a very simple question, but I haven't been able to find a good answer. When working with analytical signals in general, and software defined radio in particular, a common operation is to ...
1
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1answer
63 views

complex multiplier in divide and combine FFT

I am studying radix 2 algorith from Proakis' book. But I'm a bit confusied why 1st DFT $G_1$ is not multiplied by complex entity while 2nd DFT $G_2$ is being multiplied by complex entity $W$ as shown ...
2
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1answer
41 views

Does a linear phase FIR filter shifted in frequency preserve linear phase?

Let's say I have a symmetric (and therefore linear phase) FIR low pass filter with real coefficients. If I then shift this filter in some direction in frequency by multiplying its coefficients with a ...
0
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1answer
68 views

How to model state space for complex valued system correctly in SIMULINK (MATLAB)?

When trying to use the default state-space model block, if there is a complex number valued in the matrices, there will be an error To resolve that, firstly I need to look at pseudo reference model ...
2
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2answers
113 views

What to do after this last step?

I am solving a question from book in which I have to use summation. It is as follows: $$ \frac{1}{10}\sum_{n=0}^{9} e^{-jk\omega_0n} $$ The value of $\omega_0$ is $\frac{2\pi}{10}$. What I ...
4
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1answer
116 views

FIR design for arbitrary magnitude and phase: Why can I separate real and imaginary parts like this?

In this question about the design of a FIR filter with arbitrary magnitude and phase specifications user robert bristow-johnson suggested to split the desired complex frequency response $H$ into its ...
1
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3answers
77 views

How the FFT takes a cosine or sine and outputs the frequencies of the complex form?

If i take the Fast Fourier Transform (FFT) of a cosine function, what has turned this cosine function into its complex exponential form which consists of $e^{i \omega t} + e^{-i \omega t}$ ? Because ...
2
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1answer
108 views

Spectrum of Cosine in Complex Form

The complex exponential form of cosine $$\cos(k \omega t) = \tfrac{1}{2} e^{i k \omega t} + \tfrac{1}{2} e^{-i k \omega t}$$ The trigonometric spectrum of $\cos(k \omega t)$ is single amplitude of ...
2
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2answers
76 views

How to test I/Q modulation with only one branch (I or Q)?

Given is a direct-conversion I/Q up- and downconverter system. Receiver and transmitter share the same (10MHz) reference and hence the LO frequency is identical and there is an (unknown) phase ...
0
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1answer
87 views

FIR filter design: evaluating the error function

Question 1 $$ H(e^{j\omega})=\sum_{n=0}^{N-1}h[n]e^{-jn\omega} =\mathbf{c}^H(\omega)\cdot \mathbf{h} \tag{1} $$ $$ =\mathbf{h}^H\cdot\mathbf{c}(\omega) \tag{2} $$ $$H(\mathbf{h})=\sum_{k=1}^Kh[k]e^{...
0
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1answer
58 views

Extracting positive frequencies of discrete-time signal

Convolution in the time domain is the same as multiplication in the frequency domain. My data is sampled at 200 Hz, which means that the Nyquist frequency is 100 Hz, and all frequency content is <=...
2
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3answers
295 views

Derivative with respect to complex conjugate

I have a real function $C$ of a complex vector $x$. While taking the gradient of the function $C$ for minimising the same, why do we take the derivatives with respect to the complex conjugate of $x$, ...
1
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1answer
44 views

Poles of the transfer function in Z Transform

Given that: $H(z)$ has 4 poles maximum. $H(z)$ has a pole at $z_1=a+bi$ Given that the impulse response $h[n]$ is: Symmetric: $h[n] = h[-n]$ Real: $\forall$$n$ , $h[n]$$\in$$\mathbb{R}$ How we can ...
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1answer
39 views

Complex FFT reversing

I've succeeded to compute complex FFT of a data array of interleaved values using the arm_cfft_f32() API of the CMSIS DSP library for Cortex-M4, and got in the same array the FFT results as frequency ...
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2answers
949 views

How to convert wave from real to complex and vice versa? [closed]

I have wave expressed by array of real numbers (double in C++). But I want to express it as a complex. I tried to create complex variable and assign to its real the ...
5
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2answers
767 views

Neural Networks and Complex Valued Inputs

[not sure if this or stats.stackexchange was the correct location for this post, so put it on both for now.] I've seen some recent papers describing complex valued neural networks like this one: Deep ...
0
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2answers
88 views

MLE parameter estimation — confusion regarding some terms in the pdf of complex normal r.v (Part 2)

This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv If $v \sim CN(0,2\sigma^2_v)$ ...
0
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1answer
25 views

Is there an equation for efficiency of a 2-radix FFT as you raise $k$?

I know the efficiency for an $N$ point 2-radix FFT is $N\log_2(N)$ but assuming $k\leq N$, what if you were looking for the efficiency of calculating $k$ positions of the FFT? Would the efficiency be $...
0
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2answers
60 views

MLE formulation — confusion regarding the terms in the equation (Part1)

If $v \sim CN(0,2\sigma^2_v)$ is a circularly complex Gaussian random variable which acts as the measurement noise in this model $$y_n = x_n + v_n \tag{1} $$ where $x \sim CN(0,2\sigma^2)$, then is ...
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2answers
1k views

Even and odd signal energy property

In Signals and Systems by A. V. Oppenheim, A. S. Willsky, S. Hamid Nawab, 2nd Edition, and Signals and Systems, Simon Haykins, Barry Van Veen, 2nd Edition there is a problem related to energy of real-...
4
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2answers
695 views

Discontinuities in the FFT

So I am taking the Fast Fourier Transform of the following function: $$ x[n] = \displaystyle\sum\limits_{i=0}^{5} A_{i} \cos\left(\frac{\omega_{i}}{\omega_{s}} n + \phi_{i}\right) $$ Where the ...
1
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1answer
63 views

Question regarding DTFT of a complex signal

I have been doing DTFT practice problems for my DSP course, and I encountered this problem in the textbook that completely stumped me. The question asks to find the DTFT of the shown signal and to ...
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0answers
69 views

I want to understand the Dual Tree Complex Wavelet Transform

I want to understand the dual tree complex wavelet transform for vibration analysis of motor faults.I search a lot of books and materials but couldn't understand Can anyone recommend me a book or ...
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2answers
1k views

Finding the fundamental frequency of a periodic signal

Suppose we have the signal $$x(t) = e^{j\omega_1 t} + e^{j\omega_2 t} + e^{j\omega_3 t},$$ where all the frequencies are rationally related (that is, the ratio of any pair of frequencies is a rational ...
0
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1answer
284 views

How to eliminate negative frequencies from IQ signal

I have a 192kHz IQ signal from an RF receiver, and i'm trying to remove signals in the negative (or positive) frequency spectrum. I see that the negative frequency signals are -90 degrees phase ...
1
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1answer
97 views

How do you show the Discrete Time Fourier Transform of $x[n]=\cos(2\pi f_0n)$ is $ \frac{1}{2} \delta(f+f_0) + \frac{1}{2}\delta(f-f_0)$? [duplicate]

How do you show the Discrete Time Fourier Transform of $x[n]=\cos(2\pi f_0n)$ is $ \frac{1}{2} \delta(f+f_0) + \frac{1}{2}\delta(f-f_0)$? Here is my thought process: The definition of DTFT in my ...
0
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0answers
45 views

equivalency between cross-spectrum and covariance of band-limited analytic signals

I have worked out through experimentation that for phase-shifted pure sinusoids $x(t)$ and $y(t)$ of frequency $f$, the (complex) cross-spectrum $\Gamma_{x,y}(f)$ is numerically equivalent to the ...
1
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2answers
110 views

MMSE - How to minimize a complex error with respect to a set of real parameters

Suppose there's a complex signal $X(k)$ (where $k \in \{0, 1, 2,...,N - 1\}$) corrupted by additive complex noise. Its estimate $\hat{X}(k)$ is a linear combination of a set of real parameters $A_r$ ($...
1
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1answer
130 views

How to extract single side of signal spectrum in SIMULINK

Signal spectrum have two side, positive and negative. I want to make these separate in two signal, by MATALB SIMULINK. But how? I can't find it's block on DSP or communication toolbox. I found a block ...
7
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3answers
2k views

Replacing “e” in Euler's formula with another number

Does Euler's formula remain valid if we use any real number other than the constant $e$? For example replacing $e$ with 5 would make the formula look like this: $5^{it}$. I tried this idea in ...
3
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1answer
418 views

Complex IIR to Real IIR

I have created an IIR design algorithm that generates complex coefficients (there is no symmetry in the poles and zeros). However, the IIRs will be used to filter a real signal. Is there a closed form ...
0
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1answer
335 views

Calculating poles with complex numbers and quadratic equation

given: $z^2 + 0.8 \sqrt2 z + 0.64 = 0 $ Then, I am using the quadratic equation: $ z_{1,2} = \frac{-0.8 \sqrt2 \pm \sqrt{(0.8\sqrt2)^2-4 \cdot 0.64}}{2} $ Wolfram Alpha says it the end there should ...
0
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1answer
59 views

What is special about the frequency $\omega_0=\pi$ that suddenly causes rate of oscillation decrease?

In Alan Oppenheim's book Signals and Systems a comparison is made between the properties of discrete-time and continuous-time complex exponential signals in section 1.3 pg. 26. Specifically it says: ...
0
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1answer
99 views

Confusion about subtle difference between discrete-time and continuous-time

In Alan Oppenheim's book Signals and Systems a comparison is made between the properties of discrete-time and continuous-time complex exponential signals in section 1.3 pg. 26. Specifically it says: ...
4
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1answer
596 views

How do I convert a real baseband signal to a complex baseband signal?

I have radio telescope observations that have resulted in two real-valued signals (corresponding to the right- and left-handed circular polarizations). The signals are sampled at rate $2B$, and ...
1
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1answer
53 views

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 ...
2
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1answer
95 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
587 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
910 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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0answers
15 views

Autocorrelation of an ECB process

While I was reading through a content for Signal Processing, the formula for evaluating autocorrelation for an Equivalent Complex Baseband Stochastic Process is given as: I want to know how to write ...
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1answer
452 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
464 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 ...
3
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4answers
2k 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 ...