# 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 ...
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 ...
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 ...
457 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 ...
98 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 ...
251 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 ...
116 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 ...
85 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/...
2k 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 ...
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 ...
577 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. ...
102 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 ...