# Questions tagged [optimal-filter]

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### Constrained Least Squares Filter Design

I would like to design a complex FIR filter, $h$, for a known signal that produces a desired output: $d$ = $s*h$ (where $s$ is my signal and $d$ is the desired filter output). Let $S$ be the ...
206 views

### How to derive the "well-known" solution to Unconstrained Array Gain?

Can someone point me to a webpage or other resource that shows how to analytically solve the beamformer Unconstrained Array Gain expression in Henry Cox's 1987 IEEE paper "Robust Adaptive ...
571 views

### Complex Least Squares Approximation

In the case of frequency domain FIR filter design, the error function given by : $$E(\omega)=H(e^{j\omega})-D(e^{j\omega}) \tag{1}$$ is a linear function with respect to the unknown filter ...
33 views

### Given the following signalling elements design the optimum receiver?

Given the following signaling elements, \begin{align} g_1(t) &= A \quad \text{for} \quad -T/4 < t \leq 0 \\ g_2(t) &= A \quad \text{for} \quad 0 < t \leq T/4 \\ g_3(t) &= A \quad \...
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### What is the optimal filter?

I am currently working on a problem on filtering. In fact, let's suppose a signal that is expressed as : $r(t) = z(t) + x_i(t)$, where $z(t)$ is a smooth function and $x_i(t)$ is white Gaussian noise. ...
148 views

### Minimizing Time Sidelobes with Pulse Compression

I am trying to compute a compression filter function to minimize the error from a a desired pulse compression result. The usual approach to doing this is to minimize the RMS error of the the ...
1 vote
62 views

### Optimal receiver for a binary system employing waveform $s=A\cos^{2}(\pi f_c t \pm \alpha)$

I want to design an optimal (minimizing error probability) receiver for system of two waveforms (with $0<\alpha<\frac{\pi}{2}$): \begin{align} s_1 &=A\cos^{2}(\pi f_c t + \alpha)\\ s_2 &=...
1 vote
84 views

### Extended Kalman Filter in mechanics, electronics and hydraulics?

Extended Kalman Filter is most used in GPS and navigation systems. But how much do I gain to switch to Extended Kalman Filter to the linjear Kalman Filter if I do LQGI controller for the industry? ...
27 views

### Least squares filter with non-linear phase and independent weights for phase and magnitude

Intro My question is related to a previous one linked here. I am interested in non-linear phase FIR filters with a specific desired phase response. After I tried the options in the linked question I ...
178 views

### Degradation of BPSK system using matched filter with a timing error

Given a BPSK system with: \begin{align*} s_1(t) &= Au_T(t) \\ s_2(t) &= -Au_T(t) \\ \end{align*} where $u_T(t)=1$ for $0<t<T$, and zero otherwise. Given $A > 0$, and Gaussian white ...