Questions tagged [complex]

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How to derived an equivalent real-valued system model of the complex value MISO system with beam forming?

Currently I am interested in finding the equivalent real value model of the following system with beam forming vector $y = h \times \mathop {{w_1} \times {x_1}}\limits_{{\text{WANTED}}\,\,{\text{...
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1answer
25 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 ...
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2answers
84 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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1answer
95 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 ...
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26 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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4answers
78 views

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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2answers
725 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
93 views

For Schwarz inequality for 2 signals $s_1(t)$ and $s_2(t)$, equality holds if $s_1(t) = c\cdot s_2(t)$ ($c$ is constant). Does $c$ have to be real?

I tried for 2 signals $s_1(t) = u(t)$ and $s_2(t) = (1+i) \cdot u(t)$. $i$ is the complex unit ($i = (-1) ^{0.5}$). I got the left hand side of the inequality as $(1-i)$ and the right hand side as $(...
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1answer
43 views

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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1answer
53 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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1answer
24 views

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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2answers
47 views

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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1answer
4k views

What would be the variance for complex number?

When $x$ is a zero mean random variable then $$\sum_{n=1}^N x_n x_n^T = N \sigma^2_x\,\text,$$ where the variance is $\sigma^2_x$. I'm considering Complex Normal Distributions where the real and ...
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1answer
1k views

Confusion regarding pdf of circularly symmetric complex gaussian rv

Considering a random variable $x$ that takes in values from a complex domain. Its real and imaginary components are totally uncorrelated. I am following this link and also studying this document. In ...
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1answer
44 views

Finding poles of an abstract transfer function

When finding the poles of something like the following transfer function, would I be able to write $z=\sqrt[L]{\mu}$ since square roots aren't technically defined on the complex plane? $$Y(z) = \frac{...
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12 views

USRP N210 and FFT

I am getting IQ data from my usrp N210. It has been written in a file as a complex number and I can analyze it with matlab. The IQ data actually resembles the power of my processor. The sampling ...
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1answer
35 views

std::cosf fluctuation: Results are off in low frequencies [closed]

I attempted to generate a continuous wave signal by using the C++ cos/sin functions. It's partly successful, meaning high frequencies seems ok, but very low frequencies give unexpected results. The ...
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2answers
121 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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3answers
2k views

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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9answers
1k views

Efficient Magnitude Comparison for Complex Numbers

Is there a more efficient algorithm (or what is the most efficient known algorithm) to select the larger of two complex numbers given as $I + jQ$ without having to compute the squared magnitude as $$...
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1answer
52 views

Complex time domain signals and QAM

Is there an inherent connection between complex time domain signals and QAM? Given a complex time-domain signal is it always implied that this is a QAM-demodulated form of a real time domain signal? ...
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2answers
71 views

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 ...
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4answers
899 views

Compression algorithms specific to complex signals

I am looking for (lossy or lossless) compression algorithms dedicated to complex signals. The latter could be composite data (like the left and right for stereo audio), a Fourier transformation or an ...
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1answer
71 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
330 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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26 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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3answers
4k views

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
74 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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0answers
23 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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0answers
61 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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0answers
40 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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1answer
121 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
95 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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2answers
730 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
3k 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
358 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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2answers
3k 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
132 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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2answers
123 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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0answers
42 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
981 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
96 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
215 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
3k 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
407 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
4k 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
1k 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
379 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
112 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
3k 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 ...