📘 signal processing

1. **Problem:** Find the Z-transform $Z(n)$. 2. **Formula and explanation:** The Z-transform of a sequence $x_n$ is defined as $$Z\{x_n\} = X(z) = \sum_{n=0}^\infty x_n z^{-n}.$$

1. **Problem Statement:** Determine the Fourier series of a triangular waveform $x(t)$ with amplitude $A$ and period $T=2\pi$. 2. **Fourier Series Formula:** For a periodic functio

1. The problem is to understand the MATLAB code snippet involving signal processing operations. 2. The code defines a vector $b$ as a product of several components: a scaled sinc f

1. **Problem Statement:** Verify if the MATLAB function implementing a transmit filter using FIR filtering is correct. 2. **Understanding the Code:**

1. **State the problem:** We are given the power spectral density (PSD) of a process as $$S_{xx}(\omega) = \frac{\omega^2 + 9}{\omega^4 + 5\omega^2 + 4}$$ and asked to find the mea

1. The problem asks to find the power spectral density (PSD) of a stochastic process, which describes how the power of a signal or time series is distributed over frequency. 2. The

1. **State the problem:** We want to analyze the function $$S_{xx}(\omega) = \frac{\omega^2 + 9}{\omega^4 + 5\omega^2 + 4}$$ which represents a power spectral density function. 2.

1. **Problem Statement:** Find the power spectral density (PSD) of a random process whose autocorrelation function $R(\tau)$ is given by:

1. **Problem Statement:** We have a message signal $$m(t) = \begin{cases} 3\cos(50\pi t) + \sin(10\pi t), & t \leq 2 \\ 0, & t > 2 \end{cases}$$

1. Muammo bayoni: Signallar filtratsiyasi va tahlilida funksional qatorlar tatbiqlari mavzusida qisqacha referat yozamiz. 2. Funksional qatorlar nima? Bu - funksiyalar ketma-ketlig

1. Muammo bayoni: Signallar filtratsiyasi va tahlilida funksional qatorlar tatbiqlari mavzusida referat yozish va uni himoya qilish uchun asosiy tushunchalar va matematik asoslarni

1. **Problem Statement:** Given the discrete-time signal $x[n] = (n+1)\left(\frac{1}{4}\right)^n u[n]$, where $u[n]$ is the unit step function, analyze or describe the signal.

1. **Problem Statement:** We need to find a structure realization for the linear phase FIR filter given by the transfer function: $$H(z) = \frac{1}{2} + \frac{1}{4}z^{-1} - \frac{1

1. **State the problem:** We want to calculate the coefficient $b_n$ for a signal defined by the piecewise integral $$b_n=\frac{2}{T}\left[\int_0^{\frac{T}{4}} 5 \sin(2\pi n f t)\,

1. Problem statement: You have spectral measurements from multiple cameras that observe the same objects but differ in sampling rate, time alignment, and spectral resolution, and y

1. The problem describes frequency domain data collected from different cameras capturing the same objects. 2. The data varies due to differences in camera properties: some cameras