Mathlab Project

jrtn04
timer Asked: Mar 8th, 2016

Question Description

I need this project to be written in Mathlab.

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EE2347 Project #1 (Team of 3) Mathematical Models and MATLAB Programming Due Date: 3/10/2016 (Thursday) Title: The Magic Kernel Background: Mathematical models described by the following integral equations occur in many applications in electrical engineering, y (t ) = ∫ ∞ −∞ x (τ ) k ( t − τ )dτ = ∫ z (t ) = ∞ −∞ ∫ ∞ −∞ x (τ ) k ( −τ + t )dτ x (τ + t ) k (τ )dτ (1) (2) where x ( t ) represents the given/input signal, y ( t ) and z ( t ) represent the resulting/output signals, and k ( t ) is the kernel, which may represent a system impulse response, a template, etc. Since these mathematical models are widely used in electrical engineering (and also in other fields), they are given special names; Equation (1) is called the convolution integral and Equation (2) is called the correlation integral. In discrete forms, the convolution and correlation integrals can be approximated using series summations as shown in Equation (3) and Equation (4), respectively. y ( n ) = ∞ ∑ x ( m ) k (−m + n) (3) ∑ x! ( m + n) k! ( m ) (4) m=−∞ ∞ z! ( n ) = m=−∞ Equation (3) and Equation (4) are called discrete convolution and discrete correlation, respectively. In Eq. (3) and Eq. (4), x , y , and z are the discrete-time (time-sampled) signals, and k is the discrete-time kernel. Objective: The objective of this project is to explore the effects of selected kernels on audio signals using discrete convolution and discrete correlation. Project parameters and minimum requirements: The analog audio signal must be bandlimited to 15 kHz and the sampling rate, Fs , is set at 33,600 samples/sec. The minimum length of the sound signal is 10 seconds. Effects of the following kernels on the input sound signals must be investigated: ⎧⎪ 10 (Fs + 1), − ⎢ F 20 ⎥ ≤ n ≤ ⎢ F 20 ⎥ ⎣ s ⎦ ⎣ s ⎦ k1 ( n ) = ⎨ 0, elsewhere ⎪⎩ ⎧⎪ sin ( n χ ) ( nγ ) , − ⎢ F 20 ⎥ ≤ n ≤ ⎢ F 20 ⎥ ⎣ s ⎦ ⎣ s ⎦ k2 ( n ) = ⎨ 0, elsewhere ⎪⎩ ⎧⎪ sin ( n χ ) , − ⎢ F 20 ⎥ ≤ n ≤ ⎢ F 20 ⎥ ⎣ s ⎦ ⎣ s ⎦ k3 ( n ) = ⎨ 0, elsewhere ⎩⎪ where Fs = 33600 samples/sec , χ = 6000π Fs , and γ = 2π Fs . (5) (6) (7) Develop and implement an algorithm in MATLAB to compute the discrete convolution and discrete correlation, and play the input and output audio signals. The input audio signals are stored in WAV (or ASCII) files. Your program shall prompt the user for file names of the input and output audio signals (WAV files) and the ASCII file (text file) for the kernel. Your program shall (1) read/load the input audio signal and the kernel, (2) play the input audio signal, (3) plot a section of the input signal (in time domain), (4) perform the convolution and correlation operations, (5) plot a section (similar section/time-interval as in (3)) for each output signal, (6) store the output signals in the specified files. Computational tool: • • Mathematical background: Convolution, correlation, and filtering MATLAB functions: matrix/array operations. You MUST CREATE your own discrete correlation and discrete convolution functions using basic MATLAB commands and vector programming approach. You are encouraged to study the conv() and xcorr() functions and use them to validate your correlation and convolution functions. NOTE: conv() and xcorr() can only be used to validate the functions you created! Tasks: 1. Develop a high level algorithm (sketch the flowchart) for this project; identify major functions/operations for the entire program. 2. Develop and validate a computer method and codes to perform the discrete convolution and discrete correlation. 3. Record/select at least 3 types of audio signals: speech, symphonic music, and pop/vocal music 4. Analyze and present the results using the three given kernels (thus, at least 9 cases). 5. Design and experiment with other kernels; analyze and present the results. 6. Submit a project report (in MS Word) with at least the following sections (i.e. follow the IEEE format): - Abstract of this study - Introduction (i.e. address Who cares? What has been done? And what you are proposing) - Theory section which includes (i) brief description of the concepts of convolution and correlation (ii) brief description of your methods to compute the convolution and correlation - Validation and result analysis (i.e. show that your approach/method works) - Summary/Conclusions of this project 5. Submit the project report (printed copy) in class and email the GTA the electronic file for the report along with the complete MATLAB program. 6. Provide a 10-minute presentation and demonstration of your project during the lab/class sessions. REMINDER: This should be a fun and interesting project ... BUT … Your team needs to start working on the project as early as possible; it takes time! If your team has any question (or difficulty) please see the GTAs or me as soon as possible.
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