# Questions tagged [complex]

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49 views

### Pole locations of Butterworth filter

I am reading Proakis book "DSP using Matlab", 3rd edition. I am reading chapter 8, section 8.3, p. 402, and I am confused regarding the equation of poles (roots of denominator of system ...
33 views

### Max frequency of cosine in SDR

I would like to transmit a 56 MHz real cosine and receive it using SDR with max complex sample rate equals 61.44MSPS and an analog filter with BW = 56MHz (the transceiver is AD9361). Can I do it? How ...
1k views

### Are there any real world applications for complex-valued signals or impulse responses?

I was just curious... $$x[n] {\longrightarrow} \boxed{h[n]} {\longrightarrow} y[n]$$ I've never seen a real world filter where the coefficient of $h[n]$ were complex, or where $x[n]$ was a complex ...
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### A hypercomplex encoding to preserve spatial/temporal information? [closed]

I have recently come across the idea of encoding a 1D signal (i.e. a mono audio) as a complex vector instead of as a vector of reals, where the imaginary part is used to encode the cells' positions. ...
28 views

### Complex Data type not accepted in Simulink

I am having an issue with the interaction of the Matlab function block in the Simulink with my model block. Below you can also find the picture. I have created a Matlab function with three inputs and ...
98 views

### Why are the real- & imaginary part of complex white gaussian noise independent processes?

Assume we transmit a bandpass signal over an AWGN channel adding the Gaussian noise contribution $n$ \begin{equation} Acos(\omega_ct) + n(t) \end{equation} Further, the bandpass signal is generated ...
27 views

### Filtering via Convolution and Multiplication… Why different results? *Code and image*

Image and MATLAB code are below. I am doing Complex Down Conversion (IQ Sampling) to 0 Hz and using a Low Pass Filter after it to remove an unwanted conversion product. I start with 500-1000Hz ...
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### Negative frequency in the Fourier Transform [duplicate]

Why use this instead of a positive frequency? I asked on the math forum but it just wasn't helpful. I understand the idea of a negative frequency is important in general since many real signals like ...
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### Possibilities to get the amplitude of a signal at specific frequency from IQ

I'm newbie to the dsp topic and my understanding of math symbols is limited. So at the moment I'm little bit lost to find the right resources. I receive an IQ stream from a SDR. Sample rate: 250k/s ...
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### Are the components of a Bandpass signal namely “inphase” and “quadrature” real functions in time domain?

A band pass signal representation goes by the generalization as $X(t)=XX(t)*e^{j \cdot2\pi \cdot ft}$ where $f$ be the carrier freq. and $XX(t)$ be the complex envelope. On further decomposition it ...
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### Why does my digital upconversion result in two tones?

I am using Xilinx's RFSoC in I/Q mode. The important point is that in the digital space I have real and complex samples. I take the incoming data and multiply it by a complex sinusoid. In my test ...
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### Intuitive meaning of complex time domain signal representation (quadrature sampling)

I saw What is the meaning of imaginary values in the time domain?. My question is about I Q samples as recorded from an SDR receiver (e.g. RTL-SDR). My understanding is that we can call these I Q ...
75 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 ...
373 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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### 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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### 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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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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### 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 ...
64 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 ...
126 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 ...
98 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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### 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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### 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 ...
366 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 ...
138 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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### 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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### 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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### 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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### 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 ...
1k 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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### 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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### 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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### 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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### 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 ...