Questions tagged [complex]

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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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57 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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71 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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164 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
885 views

Use of complex numbers to calculate Doppler effect?

First of all, I'm a beginner in this field, please tell me if any of what I'm asking is too basic / can be found with some google research. I have a situation with a static TX and a moving RX (v is ...
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4answers
76 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
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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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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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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1answer
950 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
230 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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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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1answer
307 views

Covariance matrix $P$ and $Q$ for complex valued data

The equations for the Kalman filtering are IM = H*X; IS = (R + H*P*H'); K = P*H'/IS; X = X + K * (y-IM); P = P - K*IS*K'; The covariance matrix in my ...
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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
318 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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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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1answer
73 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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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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1answer
511 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
211 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: ...
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1answer
408 views

MATLAB's $\tt filter()$ function for complex valued data [closed]

I want to use the filter() function to implement an FIR filter having complex data values as the input to it. For real, I used this function as ...
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1answer
97 views

Is it possible to Denormalize a matrix of complex numbers?

In this article, FFT and I-FFT are achieved as the following: FFT steps process starts with a Bitmap image. Bitmap-image to Integer-image Integer-image to Complex-image Apply Forward-FFT to Complex-...
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1answer
2k views

How to perform an FFT on a signal with a sampling rate of 44100?

This is probably a very simple Signal Processing question but I can't quite work it out. I'm currently writing an android app which needs to perform an fft on audio data taken from the phone's ...
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25 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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8 views

How to derived an equivalent real-valued system model (receiver signal model) of the complex value MISO system?

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
23 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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1answer
42 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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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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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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1answer
52 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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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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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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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
81 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
628 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
121 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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2answers
722 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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1answer
722 views

Filtering/Analyzing Complex Data stream

I receive complex I and Q data from an USRP. I want to do a Hamming window LP filter on the data. However, I don't get the grasp of how I use the complex data. It is unusual because most of the time ...
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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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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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