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# How to generate an AM signal using sampled signal using Matlab

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How to generate an AM signal using sampled signal using Matlab

Time and frequency domain representation of signals are concepts that is essential in understanding the characteristics of amplitude and frequency modulated signals. Many electrical engineering technology communications text books do not convey some of the important characteristics of complex signals [1], [2], [3]. The ability to modify parameters and immediately see their effect on the time and frequency representation of a signal is invaluable in understanding communication signals.

Sampling a Time Signal

Time domain representation of signals in MATLAB is analogous to a discrete time signal. Each increment of time represents a sample of a continuous waveform. The size the of time increments, nT, determines the maximum unambiguous frequency of the sampled signal. The Nyquist rate is the sampling frequency required to unambiguously sample a signal of maximum frequency content fmax [5]. The Nyquist rate is defined below:

fs 2fmax

The time increment is T=1/fs. In these simulations, the carrier is displayed at the center of the plot, therefore the sampling rate will be:

f s 4 f c

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### How to generate an AM signal using sampled signal using Matlab

1. 1. INNOVATION in Communication systems & Circuits - ITopic: How to generate an AM signal using sampled signal Made by:- Sushil Kumar Mishra (ECE-I) Roll no. : 05311502809 1
2. 2. IntroductionTime and frequency domain representation of signals are concepts that is essentialin understanding the characteristics of amplitude and frequency modulated signals.Many electrical engineering technology communications text books do not conveysome of the important characteristics of complex signals [1], [2], [3]. The ability tomodify parameters and immediately see their effect on the time and frequencyrepresentation of a signal is invaluable in understanding communication signals.Sampling a Time SignalTime domain representation of signals in MATLAB is analogous to a discrete timesignal. Each increment of time represents a sample of a continuous waveform. Thesize the of time increments, nT, determines the maximum unambiguous frequencyof the sampled signal. The Nyquist rate is the sampling frequency required tounambiguously sample a signal of maximum frequency content fmax [5]. TheNyquist rate is defined below:fs > 2∗ fmaxThe time increment is T=1/fs. In these simulations, the carrier is displayed at thecenter of the plot, therefore the sampling rate will be:f s = 4∗ f cThe Fast Fourier TransformThe frequency content of a discrete signal may be determined by its discreteFourier transform. 1
3. 3. The FFT transform routine in MATLAB is implemented two ways. If the numberof samples N is a power of 2, the FFT routine used a radix-2 fast Fouriertransform algorithm. If N is not a factor of two, a slower mixed radix algorithm isused. An n-point FFT may also be specified. If n < N then the samples aretruncated, if n > N then the samples are padded with zeros [4]. The number ofsamples N determines the frequency resolution of the Fast Fourier Transform(FFT). The frequency resolution of the FFT is:The amplitude of the FFT must be properly scaled.The amplitude depends on the number of samples.The result of the FFT operation is a vector of length N, only half of the vector isneeded to covey the frequency content of the signal, the other half is symmetrical.AM Waveforms 1
4. 4. The time domain representation of a signal is familiar to students. It is the mostcommon way to represent a time varying signal. An amplitude modulated (AM)waveform in the time domain has the following formThe overall signal can be described by: More commonly, the carrier amplitude is normalized to one and the am equation is written as: In most literature this expression is simply written as:This is for a single frequency modulating signal. This example is what most textsuse in explaining AM modulation. In practice however, most modulating signalsare composed of many frequencies each with a unique amplitude. Using MATLABis easy to create such a signal and analyze its time and frequency representations. 1
5. 5. Simulink Circuit diagram: 1
6. 6. Output AM wave (In case of sinusoid input)2) In case of square input 1
7. 7. 3) In case of sawtooth inputResult:AM wave has been studied and generated using sampling criteria.Moreover the result is verified for sinusoidal, square & sawtooth inputwaveforms.Bibliography: 1) Internet 2) Text books 1
8. 8. _____________________ ( Teacher Incharge)1