Fm modulation and demodulation matlab code

Matlab

Content:

Amplitude Modulation and Demodulation

Frequency Modulation and Demodulation

Sampling and Reconstruction of Lowpass Signals

Generation PCM Signals

Delta Modulation

Amplitude Modulation and Demodulation :

In our MATLAB program we generate the AM signal with the modulation index of μ=1, By using the message signal m1(t)

MATLAB code ExampleAMdemfilt.m generates the message signal, the corresponding AM signal, the rectified signal in noncoherent demodulation, and the rectified signal after passing through a low-pass filter

The lowpass filter at the demodulator has bandwidth of 150 Hz.

Amplitude Modulation and Demodulation : (Cont.)

Notice the large impulse in the frequency domain of the AM signal

No ideal impulse is possible because the window of time is limited, and only very large spikes cantered at the carrier frequency of ±300 Hz are visible.

In addition, the message signal bandwidth is not strictly band-limited.

The relatively low carrier frequency of 300 Hz forces the LPF at the demodulator to truncate some message components in the demodulator

Amplitude Modulation and Demodulation : (Cont.)

Distortion near the sharp comers of the recovered signal is visible.

Note: triangl is the function (triangl.m file) used in the MATLAB code, Please make sure that the function is save in the relevant path for access(where you save your MATLAB code)

FM modulation and demodulation:

In telecommunications and signal processing, frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave.

This contrasts with amplitude modulation, in which the amplitude of the carrier wave varies, while the frequency remains constant.

The FM coefficient is kf = 80 and the PM coefficient is kp = π. The carrier frequency remains 300 Hz.

FM modulation and demodulation: (Cont.)

The frequency domain responses will have higher bandwidths of the FM and PM signals when compared with amplitude modulations.

Note: triangl is the function(triangl.m file) used in the MATLAB code, Please make sure that the function is save in the relevant path for access(where you save your MATLAB code)

FM modulation and demodulation: (Cont.)

Upon applying the rectifier for envelop detection, we see that the message signal follow closely to the envelope variation of the rectifier output.

Finally, the rectifier output signal is passed through a low—pass filter with bandwidth 100 Hz. We used the finite impulse response low—pass filter of order 80 this time because of the tighter filter constraint in this example.

The FM detector output is then compared with the original message signal.

FM modulation and demodulation: (Cont.)

The FM demodulation results clearly show some noticeable distortions.

First, the higher order low-pass filter has a much longer response time and delay.

Second, the distortion during the negative half of the message is more severe because the rectifier generates very few cycles of the half—sinusoid.

FM modulation and demodulation: (Cont.)

This happens because when the message signal is negative, the instantaneous frequency of the FM signal is low.

Because we used a carrier frequency of only 300 Hz, the effect of low instantaneous frequency is much more pronounced.

If a practical carrier frequency of 100 MHz were applied, this kind of distortion would be completely negligible.

FM modulation and demodulation: (Cont.)

Practical frequency Demodulator:

The differentiator is only way to convert frequency variation of FM signals into amplitude variation that subsequently can be detected by means of envelope detectors.

Zero- crossing detectors are also used because of advance in digital integrated circuits.

First step is to use the amplitude limiter to generate the rectangular pulse output

The resulting rectangular pulse train of varying width can then be applied to trigger a digital counter.

These are the frequency counter designed to measure the instantaneous frequency from the number of zero crossing

The rate of zero crossing is equal to the instantaneous frequency of the input signal.

Sampling and Reconstruction of Lowpass Signals:

In the sampling example, we first construct a signal g(t) with two sinusoidal components of 1 second duration; their frequencies are 1 and 3 Hz.

Note, however, that when the signal duration is infinite, the bandwidth of g(t) would be 3 Hz.

However, the finite duration of the signal implies that the actual signal is not bandwidth-limited, although most of the signal content stays within a bandwidth of 5 Hz. For this reason, we select a sampling frequency of 50 Hz, much higher than the minimum Nyquist frequency of 6 Hz.

Sampling and Reconstruction of Lowpass Signals:

The MATLAB program, Example .m, implements sampling and signal reconstruction.

The spectrum of the sampled Signal gT(t) consists of the original signal spectrum periodically repeated every 50 Hz.

NOTE: sampandquant and uniquant are function(sampandquant.m and uniquant.m file) used in the MATLAB code, Please make sure that the function is save in the relevant path for access(where you save your MATLAB code)

Sampling and Reconstruction of Lowpass Signals:

Where:

Source or input signal:

sig_in = incoming signal

L =Quantization level (16 bits encoding)

td= original sampling rate

ts= new sampling rate

s_out= sampled signal

sq_out= up sampling (gives the original sampling info)

sqh_out= results 16 bit encoding by creating matrix

Sampling and Reconstruction of Lowpass Signals:

Nonideal Practical Sampling Analysis:

Thus far, we have mainly focused on ideal uniform sampling that can use an ideal impulse sampling pulse train to precisely extract the signal value g(kTS) at the precise instant of t = kTs.

In practice, no physical device can carry out such a task.

Consequently, we need to consider the more practical implementation of sampling.

This analysis is important to the better understanding of errors that typically occur during practical A/D conversion and their effects on signal reconstruction

Sampling and Reconstruction of Lowpass Signals: (Cont.)

Practical samplers take each signal sample over a short time interval Tp around t = kTs In other words, every Ts seconds, the sampling device takes a short snapshot of duration Tp from the signal g(t) being sampled.

This is just like taking a sequence of still photographs of a sprinter during an 100-meter Olympic race.

Much like a regular camera that generates a still picture by averaging the picture scene over the window Tp.

Generation PCM Signals:

The function sampandquant.m executes both sampling and uniform quantization simultaneously.

The sampling period ts is needed, along with the number L of quantization levels.

To generate the sampled output s_out, the sampled and quantized output sq_out, and the signal after sampling, quantizing, and zero-order-hold sqh_out.

Generation PCM Signals: (Cont.)

In the first example, we maintain the 50 Hz sampling frequency and utilize L = 16 uniform quantization levels.

The results the PCM Signal. This PCM signal can be low-pass-filtered at the receiver and compared against the original message signal .

The recovered signal is seen to be very close to the original signal g(t).

Generation PCM Signals: (Cont.)

To illustrate the effect of quantization, we next apply L = 4 PCM quantization levels.

It is very clear that smaller number of quantization levels (L = 4) leads to much larger approximation error

Delta Modulation:

Sample correlation used in DPCM is further exploited in delta modulation (DM) by oversampling (typically four times the Nyquist rate) the baseband signal.

This increases the correlation between adjacent samples, which results in a small prediction error that can be encoded using only one bit.

In comparison to PCM and DPCM, it is a very simple and inexpensive method of A/D conversion

Delta Modulation: (Cont.)

A 1-bit codeword in DM makes word framing unnecessary at the transmitter and the receiver.

This strategy allows us to use fewer bits per sample for encoding a baseband signal.

To illustrate the effect of DM, the resulting signals from the DM encoder.

This example clearly shows that when the step size is too small (Δ1), there is a severe overloading effect as the original signal varies so fast that the small step size is unable to catch up.

Delta Modulation: (Cont.)

Doubling the DM step size clearly solves the overloading problem in this example.

However, quadrupling the step size (Δ3) would lead to unnecessarily large quantization error.

This example thus confirms our earlier analysis that a careful selection of the DM step size is critical.