Questions tagged [complex]

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

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 modulate it by 0.5 degrees, will this work?...
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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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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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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
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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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
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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3answers
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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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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

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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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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1answer
75 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
70 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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267 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
812 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
210 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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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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34 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
95 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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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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31 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
398 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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1answer
87 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
110 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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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
233 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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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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1answer
380 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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3answers
113 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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2answers
84 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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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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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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121 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
71 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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1answer
96 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
57 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

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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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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125 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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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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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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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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813 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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1answer
486 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
163 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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139 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
581 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 ...