# EASP Noise Ratio is a calculated value that

EASP PROJECT REPORT

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Introduction:

Analog to Digital Converter:

Real world is always analog. Analog
to Digital Converters(ADC) provides an interface between the real world and the
digital world by converting the analog signals to digital signals.

Digital to Analog Converter:

Digital to Analog Converters(DAC)
takes a digital code as its input and produces an analog voltage or current as
its output. This analog output is proportional to the digital input.

Flow chart:

The structure of
our project is given as below.

Code and Description:

1.     Analog to Digital Converter:

The input analog signal is generated
for 1000 samples using the function ‘gensumsin’. Then a random noise is
generated and added to the original analog signal. The plots of analog signal
with and without noise is presented below:

The next step would be to sample the
acquired analog signal. Sampling is the reduction of a continuous-time signal
to a discrete-time signal. A sample is a value or set of values at a point in
time and/or space. Sampling is done to convert the continuous signal into its
discrete form. It is done before quantization so that each sample can be
represented by 8 digits corresponding to 128 levels of quantization. The code
presented below was used to do the same.

The results obtained from sampling
the analog signals (with and without noise) is shown below:

The final step of ADC would be to
quantize the sampled signals obtained from sampling. Quantization is
done to replace each real number with an approximation from a finite set of
discrete values (levels), which is necessary for storage and processing by
numerical methods. The code dedicated to this process is as shown below:

The
output plots (shown below) obtained from this process is the output of the
Analog to Digital Converter.

We then calculated the SNR ratio for
the ADC outputs (with and without noise) to compare and analyze the results. Signal
to Noise Ratio is a calculated value that represents the ratio of rms signal to
rms noise.

The SNR value obtained for the
output with noise was approximately equal to 18dB whereas the SNR value
calculated for the output without noise was approximately equal to 50dB. If a
signal has greater value of SNR, it is said to be good signal. From this, we
can interpret that the output without noise was the better case of the two.

2.     Digital
to Analog Converter:

The output of Analog to Digital
converter is then used as the input of the Digital to Analog converter.

We use low pass filtering method to
obtain the original analog signals. The signal is passed through a
properly designed filter that reconstructs the original analog wave form from
its digitally coded counterpart. Here,
we have used the fir filter of type 1 to achieve the results. This filter was chosen because of its simple and easy
implementation, it does not distort its phase when it delays the input signal
and can be easily designed to be ‘linear phase’.

The code implemented for the filtering process is as
presented below:

The input of DAC after passing through
the filter gives us the original analog signal as its output. The output of the
Digital to Analog Converter for with and without noise are as shown below:

The comparison of the original
Analog signal with noise and the obtained output of the DAC with noise is as
shown below:

From the above plots, it is obvious
that the output of the DAC holds most of the data of the original input analog
signal.

Frequency spectrum analysis was then
performed on the output of DAC. The Fourier transform converts the time
function into a sum of sine waves of different frequencies, each of which
represents a frequency component. The spectrum of frequency components is the
frequency domain representation of the signal. The code below was used to
perform the same.

The output plots of the spectrum analysis
is as presented below:

From the above plots, we can
interpret that both the sides of the frequency spectrum (positive and negative
sides) of the output signal with noise shows more distortions than the output
without noise.

Conclusion:

The analog signal obtained as the
output of Digital to Analog Converter was very close to the original analog
signal when performed experimentally. However, practically, retaining all the
data of the original signal is not possible. It usually incurs some loss of
data.

By,

Subiksha Muralidharan,

Sundara Rajan Manoharan.

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