Questions tagged [complex]

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42 views

Why does the FFT of a complex variable create negative frequencies?

So I have a demodulator that streams out X and Y values. I use a spectrum analyzer within this demodulator instrument which plots the |FFT(X+iY)| against the frequency domain, which shows up with ...
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1answer
101 views

Amplify a signal and phase shift it by multiplying by a complex number

Still need help 25th October 2019 I have a real time domain signal contained in an array, it's just two different frequencies summed together. If I want to amplify this signal by 10 and phase ...
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2answers
51 views

How would one design a (quasi) linear phase adaptive notch filter for a single complex tone?

While IIR notch filters are attractive, I need to retain phase linearity at the filter output. I imagine that it's possible to use a standard IIR notch filter: https://www.researchgate.net/...
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17 views

lte matlab baseband IQ recovery

I am a beginner again to signal processing, I did my degree over ten years ago, and I am relearning all my signal processing stuff. I am a software developer by trade but now I am looking at some LTE ...
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1answer
32 views

Question about quadrature signals

My question is related to this article: https://www.dsprelated.com/showarticle/192.php I think I understand mostly everything until this sentence: "The directions in which the impulses are pointing ...
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2answers
64 views

Fractional powers of complex numbers (DSPrelated computation)

I am puzzled by this computation: https://www.dsprelated.com/showarticle/754.php (c.f. quote) Raising $ i $ to integer powers results in traversing the unitcircle in the same number of quarter ...
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19 views

Why do I need this modulo tweak to bandpass filter an I/Q signal

I have an I/Q signal with $f_c=2.06\text{MHz}$ and $f_s=50\text{KHz}$. I am looking the first 256 samples of the signal, which is a NumPY array of complex numbers. If I do a spectrogram of this ...
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31 views

Reducing hardware demands for an adaptive and complex-coefficient FIR filter

I want to implement a complex-coefficient FIR filter with adaptive coefficients in hardware (FPGA). The inputs to this filter are the I and Q channel as separate wires. The outputs are the filtered I ...
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27 views

Angular velocity of discrete time exponentials, increasing and then decreasing over 0 to 2 pi [duplicate]

So, the differences between: $$ x(t) = e^{j(\omega_{0} t) } \,\,\,\,\, \textbf{Vs.} \,\,\,\,\, x[n] = e^{j(\omega_{0}n)} $$ Are: For $x(t)$ the $\omega_{0} \to \infty $ means the oscillation rate ...
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32 views

Threshold for CAF Surface

I am calculating a time partitioned Cross Ambiguity Function (CAF) by adding the surfaces of different time-sectioned CAFs together. Meaning, I calculate a CAF using 10 seconds of IQ data, calculate a ...
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1answer
78 views

Maximum likelihood estimation complexity computation

I have a basic question about maximum likelihood (ML) estimator and its implementation. I am trying to simulate a communication system, while using ML at the receiver side to find the transmit ...
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3answers
72 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 ...
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320 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 ...
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4answers
1k 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 ...
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2answers
231 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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37 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 ...
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2answers
98 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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34 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 ...
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1answer
94 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 ...
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1answer
89 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 ...
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1answer
124 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 ...
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1answer
467 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 ...
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2answers
118 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 ...
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1answer
253 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 ...
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3answers
132 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 ...
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1answer
507 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 ...
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2answers
85 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 ...
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1answer
131 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^{...
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1answer
73 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 <=...
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3answers
1k 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 $x$, ...
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1answer
97 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
59 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
2k 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 ...
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2answers
2k 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 ...
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2answers
128 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 $v \sim CN(0,2\sigma^2_v)$ ...
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1answer
26 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 $...
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2answers
63 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
3k 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-...
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2answers
831 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 ...
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1answer
65 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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2answers
2k 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 ...
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1answer
503 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 ...
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1answer
228 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 ...
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2answers
150 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 $A_r$ ($...
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1answer
216 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 ...
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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 ...
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1answer
613 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 ...
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1answer
451 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 ...
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1answer
81 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: ...
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1answer
157 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: ...