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Questions tagged [complex]

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How to demodulate Binary Offset Carrier Signal?

I need to modulate and demodulate a BOC (Binary Offset Carrier) modulated signal. I tried starting with: ...
Dom's user avatar
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-1 votes
2 answers
90 views

Orthogonal signals basics [closed]

Suppose we have 2 orthogonal signals $x_{1}(t)$ and $x_{2}(t)$ and we add them up. Can we always say that the resulting signal will be of this form: $$x_{3}(t)=x_{1}(t)+jx_{2}(t)$$ ? If that is true ...
Root Groves's user avatar
4 votes
5 answers
841 views

How can we treat real signal as imaginary?

I'm studying MRI and I couldn't understand this assumption(?) The sentence 'The signal from one channel is no more or less "real" than that from the other channel.' Does not make sense to ...
JongYun Baek's user avatar
3 votes
1 answer
467 views

(graphic) Relation between FFT and complex signal

I have a complex signal with a frequency between 0 and 16 (16 not included). I have made four plots (in python) to show four examples. For each example I provide the signal, its FFT in both real, imag ...
Mart's user avatar
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1 vote
1 answer
138 views

Alternative to Hilbert Transform

I have an digital system that needs an analytical signal of length (in time) T. The system is sampling the analog signal with time interval delta t such that T / delta t = 128. So I have 128 samples. ...
Mart's user avatar
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please help me solve the question which proving X[N-k] is the complex conjugate of X[k] [closed]

Show for the DFT that if all x[n] are real, then X[N - k] is the complex conjugate of X[k] for k > 0. (i.e. if X[k] is a + bi, then X[N - k] is a - bi)
Reece's user avatar
  • 11
2 votes
0 answers
53 views

When converting real samples to complex, how much energy does the signal lose?

Assertion: When converting real samples to complex, the resulting complex vector will have half the energy of the original real vector. Simulation in Python tells me this is true. However, my proof ...
Jonathan Williams's user avatar
0 votes
1 answer
674 views

How can I generate a OFDM baseband signal with the output of the ifft?

I have some understanding problems with OFDM. I think I have understood most of the theoretical concept. At the moment, I am trying to write some Python code to simulate the transmitter part. This is ...
Not A Hobbit's user avatar
0 votes
1 answer
68 views

Frequency Translation after FIR Filter

I am trying to translate a signal to baseband by multiplying by the complex exponential. The issue is when I do the calculation in MATLAB the signal seems to disappear. I originally thought the signal ...
PrematureCorn's user avatar
0 votes
2 answers
820 views

Frequency shifting with complex exponential

I'm trying to frequency shift a sine wave at 50kHz by using a complex exponential at 15kHz. I should be getting an FFT with a peak at 65kHz. Instead I'm getting a strange looking peak at 52.4kHz. ...
PrematureCorn's user avatar
0 votes
1 answer
518 views

Plotting Constellation Diagrams

I'm working with some IQ data from the paper A Wideband Signal Recognition Dataset. Specifcally I've been trying to plot the constellation diagram for some the modulations within the dataset, however, ...
EpicFoodCartDestroyer's user avatar
2 votes
2 answers
61 views

System Characterization: multiply imaginary component by scalar

I tried solving a test question that frankly stumped me. If you could explain to me the solution I’d be really grateful. Given $a, b \in \mathcal{R}$ the system $R_v$ takes the complex input $a + bj$ ...
Piratemetaldrinkingcrew's user avatar
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0 answers
208 views

Problem using BladeRF using two RX inputs

I am working with BladeRF xA4. I have a signal generator at 1.5GHz modulated with cos(2pif_mt)+jsin(2pif_m*t). This generator is conected to a signal splitter. Next to the splitter two cables are ...
Luis Gonçalves's user avatar
0 votes
2 answers
213 views

Complex Envelope

Two signals have arrived with different phases. The sum signal is given by $$x(t) = A\cos(2\pi f_ct) + B\cos(2\pi f_ct + \theta)$$ What is the complex envelope of $x(t)$? Need advice on how to get ...
Gotz2bril's user avatar
2 votes
0 answers
43 views

Are real exponential signals still eigen functions of LTI systems?

I know that complex exponentials are eigen functions of LTI systems for example $e^{j2t}, e^{-j5t} , e^{j8t}$ . If we can define complex exponential as $e^{st}$ where $s$ is a complex number. Can we ...
HKTS's user avatar
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2 votes
1 answer
323 views

is this signal is perodic?

What is the time period of $$ x(t) = 7 e^{\jmath(5t + \pi/2)} + 10^{\jmath(7t + \pi/5)}$$ ? X(t) is the combination of two functions. one is the natural logarithm base, $e$, and the other is 10. if ...
Nitish's user avatar
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1 vote
1 answer
162 views

What is "spin" for the 2D (separable) Morlet?

The 2D Morlet formed separably as product of 1D Morlets, used in JTFS, is said to have "spin": $$ \begin{align} \Psi_{{\mu, l, +1}}(t, \lambda) &= \psi_\mu(t) \psi_{l}(+\lambda) &&...
OverLordGoldDragon's user avatar
1 vote
2 answers
78 views

System output in cosine notation

If I have a system with the output: $$y(t)=x(t)+0.7x(t-0.4)$$ For $x_2(t)=\cos(56t)$, how can we write $y_2(t)$ in the form $y_2(t)=A\cos(\omega t+B)$ and calculate the unknown values A, B and $\omega$...
Anna Smith's user avatar
0 votes
0 answers
113 views

Understanding FFT output oscillation around y-axis

I am looking at the output of the FFT and trying to understand the meaning of the real and imaginary parts of the output. My signals (real in time) are comprised of tonal peaks and the magnitude of ...
dale154's user avatar
0 votes
1 answer
401 views

Finding the maximum frequency deviation and phase deviation

I'm trying to solve a problem regarding communication and I'm stuck. The questions asked me to find the maximum frequency deviation are usually written in cos or sin wave. But this question isn't, so ...
wannastudycommunication's user avatar
5 votes
4 answers
345 views

Bandpass Stationary Stochastic Process

I was following this interesting post by a new user Rubem Pacelli and got stuck at Proakis' referenced definition (see Section 4-1-4 starting on page 159 here). The math, all repeated further below, ...
Dan Boschen's user avatar
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0 votes
1 answer
514 views

iq bpsk waveform generation

We have a DAC capable of being driven with IQ data (thus the bandwidth is $-f_s/2$ to $f_s/2$), and the task is to create an "arbitrary" BPSK waveform at IF. I think that means generating ...
Sittin Hawk's user avatar
1 vote
2 answers
278 views

Obtain the real part of a complex signal from imaginary part and magnitude squared

I am trying to solve a problem based on a real world measurement. Suppose I am trying to obtain a complex signal $S(x)$, but only know its magnitude squared, $|S|^2$ and its imaginary part $\text{Im}(...
Ryan's user avatar
  • 27
0 votes
0 answers
289 views

Phase Unwrapping Issue of IQ data sample in Radar Signal Processing

I am doing radar sensor signal processing. The radar sensor gives iq data corresponding to the range (sweeps). I want to detect micro motion so that phase analysis is used. Sweep is the distance ...
Rohith R's user avatar
0 votes
1 answer
211 views

Confusion about KL divergence between complex Gaussians

The KL divergence between two real-valued Gaussian distributions with means $\mu_1$ and $\mu_2$ and common variance $\sigma^2$ is well known to be: $$ D_{\text{KL}}\left(\mathcal{N}(\mu_1, \sigma^2) \...
Sami's user avatar
  • 65
1 vote
2 answers
152 views

Allpass filter with delay of $\pi/2$ for only negative frequencies

I would like to design a complex and causal allpass filter with delay of $\pi/2$, but only for negative frequencies. The positive frequencies should have a delay of 0. Is that possible and how I ...
MisterFilter's user avatar
0 votes
1 answer
95 views

Are there any recommended filter types for passband frequencies near Nyquist?

Is there a recommended filter type for frequency bands near the Nyquist frequency? I have been trying to design complex passband filter with passband $[0.8 ~~1]$ ( where $1$ corresponds to the ...
Hilbert's user avatar
  • 129
0 votes
1 answer
20 views

find gamma from complex form?

In $$e^{j\pi/\gamma x}=c$$ if $x$ and $c$ are known, how to find $\gamma$ since if we break to sine and cosine term the problem becomes more complicated. This is a complex value and $j$ indicates ...
budding_scholar's user avatar
0 votes
1 answer
41 views

Different complex pairs giving same magnitude and phase

I am trying to fit data of magnitude and phase to get complex pairs(for FFT), but I think it would be a wrong approach as different pairs of complex numbers can give same amplitude and phase , is my ...
Novice_Developer's user avatar
0 votes
1 answer
117 views

FM generation with complex numbers

Background To generate a sine wave the straight forward way is to call the sin method for each data point: Iteration (pseudo code): ...
Jay Anderson's user avatar
0 votes
1 answer
64 views

Phase of AM Signal After Mixer

Let's assume we have a carrier at $f_{c}$, and a message at $f_{m}$ ($f_{c} \gg f_{m}$). Amplitude modulation is used to modulate the message on the carrier. Let's call the modulated carrier $\text{rf}...
MisterFilter's user avatar
0 votes
1 answer
175 views

Complex Filter (Modelling a Channel ) convolved with complex baseband modulation gives error *Plots inside -Updated*

I have a complex filter that is modelling the channel response, its not symmetrical on 0. The complex filter is convolved with a complex baseband modulation of QPSK. Plot 1 Zoom in on impulse response ...
Villere_DSP's user avatar
1 vote
3 answers
2k views

Python FIR Notch filter applied on both + and - frequency but only need + frequency

I have posted a summary of what I am seeing, I just made a pulse train and testing a notch filter on it as an example only. I also have a complex baseband signal centered on 0 Hz, this complex ...
Villere_DSP's user avatar
0 votes
1 answer
148 views

converting complex sum of exponential signal to real signal

I have the following Signal model, that generates a discrete-time complex signal, where $a_k$ - amplitudes, $\phi_k$ - phases, $\alpha_k$ - damping factors and $f_k$ - frequencies are the parameters ...
Neuling's user avatar
  • 103
0 votes
0 answers
87 views

How to prove that the integral of Hilbert transform is not equal to the Hilbert transform of the integral?

To prove that $\int_{-\infty} ^\infty \mathcal{H}(g(t))(t)\text{d}t\neq\mathcal{H}(\int_{-\infty} ^\infty g(t) \text{d}t)$, where $\mathcal{H}(\cdot)$ is the Hilbert transform operator My approach to ...
UserHuffmann's user avatar
0 votes
1 answer
108 views

Can a cosine modulated complex valued baseband signal be transmitted over physical channels?

I am reading Digital Communication by Lee and Messerschmitt. In Chapter 6 on modulation, the authors say: "Modulating a complex-valued baseband signal with a cosine wave yields complex-valued ...
Userhanu's user avatar
  • 181
0 votes
1 answer
344 views

Sum of complex exponential signal in MATLAB

I want to create a sum of damped complex exponential signal with the known values of frequency $f$, damping $\alpha$, amplitude $a$ and phase $\phi$ for the $k = 1,2,...,K$ exponentials. Is there ...
Neuling's user avatar
  • 103
0 votes
1 answer
219 views

How to compute a complex modulated signal from an audio file?

I have a 30-seconds wav audio file with a sample rate of 44100Hz, obviously this array of samples is a 1D array, and so when I modulate it in AM (Amplitude Modulation) I get back a 1D array, but I ...
yarin Cohen's user avatar
0 votes
1 answer
569 views

How to separate real and imaginary part of a complex FFT?

I have an exercise where I have to calculate the FFT of a complex signal $x=l+j\cdot r$ using only one single call to a complex FFT algorithm. $l$ is the left, $r$ the right real valued vector of a ...
user230754's user avatar
0 votes
1 answer
343 views

Interpolation of complex signal

I'm struggling with particular (corner) case of interpolation of complex signal, in connection with OFDM modulation. While I assume that guard sub-carriers are always used, I'm studying a case when ...
schnajc's user avatar
0 votes
0 answers
67 views

Matrix multiplication computational complexity based on radix 2

I am wondering, can we use Radix 2 based computational-complexity calculation for any matrix multiplication whose size is $N$ x $N$ ?? where $N$ = $2^K$ and $K > 1$ is an integer ?? Or it can only ...
Fatima_Ali's user avatar
4 votes
1 answer
399 views

Tikhonov Regularization for Complex Matrices

Tikhonov regularization is used to regularize ill-posed inverse problems if the matrix $A \in \mathbb{R}^{n,m}$ to be inversed has a high condition number. For example $$ A=\begin{bmatrix}1&1\\ 1&...
Bulbasaur's user avatar
  • 209
0 votes
1 answer
257 views

Complex damped exponential signal with repetitive poles and the significance of falling factorial

I was modelling a complex damped exponential signal (discrete) with unique poles as below: \begin{equation} x = \sum_{k=1}^{K} (a_k e^{(j\phi_k)})(e^{\{(j2\pi f_k - \alpha_k)\Delta t\}t}), \quad t ...
Neuling's user avatar
  • 103
2 votes
1 answer
388 views

Compared with the real-valued continuous wavelet, what are the advantages of the complex-valued continuous wavelets?

I noticed that there are two types of wavelet functions, i.e. the real-valued, such as the Mexican hat wavelet, and the complex-valued, such as the Morlet wavelet. How was the complex-valued wavelet ...
Wang Yun's user avatar
  • 124
-1 votes
1 answer
76 views

How to write a complex symmetric gaussian signal [closed]

In my work I need to use this signal of complex symmetric gaussian noise signal represented as $w$. But I don't know exactly how to represent it
Parveen's user avatar
0 votes
2 answers
133 views

Decomposition of two equal and overlapping complex signals

I have been wracking my brain over this problem for weeks and I finally have to throw in the towel and ask for help. My background is not formally in signal processing, so I may just lack the ...
Magne Lauritzen's user avatar
2 votes
2 answers
2k views

Why is Complex Baseband better than Real Representation?

I read that one of the advantages of a complex baseband signal is that it can send more data over the same bandwidth as compared to real signal. Why is that so? If I think about it logically, doesn't ...
John Smith's user avatar
0 votes
1 answer
142 views

Energy of a complex exponential

I want to obtain the energy of this signal $$x_i(t)= e^{j2\pi(2i-1)f_0t}$$ where $f_0 = 1$ Hz, $i= 1,...,4$ and $j$ is a complex. I think I need to use the Fourier transform or the Parseval theorem ...
Marta Monteiro's user avatar
0 votes
0 answers
82 views

Let a LTI system be causal and stable with the transfer function being... show that

if the system is an IIR LTI causal and stable one, and the transfer function is \[H(z)=\sum_{n=0}^{\infty}h[n]z{^{n}}= \frac{G}{1 -\sum_{k=1}^{p}a_kz{^{-k}}}\] show that the cepstrum of this system ...
Nyquist-er's user avatar
0 votes
2 answers
652 views

Periodicity of complex exponential in continuous and discrete time (Eq 1.51, Signals and Systems by Oppenheim & Wilsky)

Hi All: This is very basic but I've always wondered about it and now I see it in print in a textbook so I may as well ask. In Signals and Systems on page 26, it says $$e^{j(\omega_0 + 2\pi)n} = e^{j2\...
mark leeds's user avatar
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