# Questions tagged [complex]

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### 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 ...
3k views

### 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 ...
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 ...
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 ...
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 ...
382 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 ...
9k views

### Considering the FFT of Real & Complex Signals

I've been implementing a website to perform the FFT of various signals, real & complex. Examining the first example, a real signal $x[n] = 10 cos(2\pi\times4n)$, I got the following FFT: Which ...
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 ...
216 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 ...
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 ...
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 ...
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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### 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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### 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 ...
2k views

### Where and how do an Image and a complex number meet?

I am trying to implement a Gabor Filter bank. Gabor Filter uses a complex function. How do the filters like Gabor Filter operate on an Image? Does a complex number represent an entire Image or only ...
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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 ...
568 views

### How should this fft output be intepreted?

I am currently reading some code, so I can understand how this FFT output is actually been stored. I have a function which computes FFT of audio file, and stores is in the format. ...
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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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$$\mathbb{R} How we can ... 1answer 72 views ### Doubts and some confusion on variance for complex rv This question is in continuation of the one asked here. Let's say that the measurement noise w or any random variable is circularly Gaussian complex. If the imaginary and real components each has ... 1answer 1k views ### Autocorrelation and Power Spectral Density (Discrete) The Autocorrelation, \phi_{aa}[\kappa], of a discrete time random process, a[k], is defined as:$$ \phi_{aa}[\kappa] = \mathrm{E}\left\{ a[k+\kappa]a^*[k] \right\} $$Taking its fourier ... 1answer 1k views ### How do you show the Discrete Time Fourier Transform of x[n]=\cos(2\pi f_0n) is \frac{1}{2} \delta(f+f_0) + \frac{1}{2}\delta(f-f_0)? [duplicate] How do you show the Discrete Time Fourier Transform of x[n]=\cos(2\pi f_0n) is \frac{1}{2} \delta(f+f_0) + \frac{1}{2}\delta(f-f_0)? Here is my thought process: The definition of DTFT in my ... 2answers 133 views ### Convolution of real with complex signal Let x[n] be real signal and y[n]=\exp(j3\pi n) be a complex signal Would the convolution between those two signals be$$x[n] * \Re(y[n]) + jx[n]*\Im(y[n])$$? 1answer 67 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 ... 2answers 179 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$A_r$($...
I have an expression for the varaince of measurement noise obtained from an estimator. The measurement noise is additive white gaussian having values in complex domain. I have squared the term $(.)^2$,...