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MODEL:Differentiation is a method to compute the rate at which a dependent output y changes with respect to the change in the independent input x. This rate of change is called the derivative of y with respect to x. In more precise language, the dependence of y upon x means that y is a function of x. This functional relationship is often denoted y = f(x), where f denotes the function. If x and y are real numbers, and if the graph of y is plotted against x, the derivative measures the slope of this graph at each point. The derivative of y with respect to x", "d y by d x", or "d y over d x". The oral form "d y d x" is often used conversationally, although it may lead to confusion. Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral is defined informally to be the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the vertical lines x = a and x = b, such that area above the x-axis adds to the total, and that below the x-axis subtracts from the total. Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign (+). Addition can also represent combining other physical and abstract quantities using different kinds of numbers: negative numbers, fractions, irrational numbers, vectors, decimals and more. Multiplication (often denoted by the cross symbol "") is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary 1

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du/dt Sine Wave Derivative Scope

1 s Integrator Scope1

1 Constant Product

Scope2

Scope5

Subtract

Scope7

Divide

Scope3

3

OUTPUT PLOTS

DIFFERENTIATION

INTEGRATOR

4

MULTIPLICATION

5

SUBTRACTION

DIVISION

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1 Con stan t

Si ne Wa ve

S in e Wav e1

Si ne W av e2

S in e Wa ve3 Sco pe 1 S in e Wa ve4

S in e Wa ve5

MULTIPLEXER

RESULTVarious types of signals ( +,*,-,/,mux,demux,integration, diffrentiation) has been studied. 7

EXPERIMENT NO. 2

AIM: To study design of Amplitude Modulation & Demodulation.

AMPLITUDE MODULATION : SIMULINK LIBRARY: Signal Processing Blockset DSP Sources DSP Constant Signal Processing Blockset DSP Sources DSP Sine wave Simulink Maths Operations Adder Simulink Maths Operations Product Signal Processing Blockset DSP SinksVector Scope

MODEL AMPLITUDE MODULATION Modulation is defined as the process by which some characteristics of a carrier signal is varied in accordance with a modulating signal. The base band signal is referred to as the modulating signal and the output of the modulation process is called as the modulation signal. Amplitude modulation is defined as the process in which is the amplitude of the carrier wave is varied about a means values linearly with the base band signal. The envelope of the modulating wave has the same shape as the base band signal provided the following two requirements are satisfied 1. The carrier frequency fc must be much greater then the highest frequency components fm of the message signal m (t) i.e. fc >> fm 2. The modulation index must be less than unity. If the modulation index is greater than unity, the carrier wave becomes over modulated

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5 DSP Constant Add Product DSP DSP Time Vector Scope

Sine Wave Sine Wave1

Output Plot

Amplitude Modulated Output

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AMPLITUDE DEMODULATION SIMULINK LIBRARY: Signal Processing Blockset DSP Sources DSP Constant Signal Processing Blockset DSP Sources DSP Sine wave Simulink Maths Operations Adder Simulink Maths Operations Product Signal Processing Blockset DSP SinksVector Scope SimulinkMath OperationsMatrix Concatenation SimulinkMath OperationsMath Function Signal Processing BlocksetFilteringFilter Designs Digital Filter Design

MODEL AMPLITUDE DEMODULATION The process of detection provides a means of recovering the modulating Signal from modulating signal. Demodulation is the reverse process of modulation. The detector circuit is employed to separate the carrier wave and eliminate the side bands. Since the envelope of an AM wave has the same shape as the message, independent of the carrier frequency and phase, demodulation can be accomplished by extracting envelope. An increased time constant RC results in a marginal output follows the modulation envelope. A further increase in time constant the discharge curve become horizontal if the rate of modulation envelope during negative half cycle of the modulation voltage is faster than the rate of voltage RC combination ,the output fails to follow the modulation resulting distorted output is called as diagonal clipping : this will occur even high modulation index.

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Horiz Cat 5 DSP Constant DSP Product Sine Wave u DSP 2 Time Matrix Concatenation T ime Vector Scope FDAT ool sqrt Math VectorFunction1 Scope2 1 DSP Constant1 2 DSP Constant2 Add1 Product1

Time Vector Scope1

Math Function

Digital Filter Design

Sine Wave1

Amplitude Demodulated Output

RESULTAmplitude modulation and demodulation is studied.

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EXPERIMENT NO. 3AIM:- To study Digital Modulation Scheme(PAM) SIMULINK LIBRARY :Communication Blockset Random Data Source Random Integrator Generator Communication Blockset Modulation Digital Baseband Modulation AM M-PAM Modulator Baseband Communication Blockset Channels AWGN Channel Communication Blockset Modulation Digital Baseband Modulation AM M-PAM Demodulator Baseband Communication Blockset Comm Sinks Error Rate Calculation Simulink Sinks Scope Communication Blockset Comm Sinks Discrete-Time Scatter Plot Scope Simulink Extras Additional Sinks Power Spectral Density Simulink Math Operations Complex to Real-img Simulink Sinks XY Graph Simulink Sinks Display

MODEL:PAM stands for Pulse amplitude modulation; it is a form of signal modulation where the message information is encoded in the amplitude of a series of signal pulses. It is an analog pulse modulation scheme in which the amplitude of train of carrier pulse is varied according to the sample value of the message signal. The signal is sampled at regular intervals and each sample is made proportional to the magnitude of the signal at the instant of sampling. These sampled pulses may then be sent either directly by a channel to the receiving end or may be made to modulated using a carrier

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