Page 36 - RTH3BA Preview

35 - ������� �������������

The algorithm that transforms time domain signals to the “discrete” frequency
domain components is called the Discrete Fourier Transform (DFT). The Fast
Fourier Transform (FFT) is an implementation of the DFT which produces almost the
same results as the DFT, but it is incredibly more efficient and much faster which
often reduces the computation time significantly. It is just a computational algorithm
used for fast and efficient computation of the DFT. Various fast DFT computation
techniques known collectively as the Fast Fourier Transform, or FFT.

Real world signals are continuous, and they contain much information that does not
contribute to the intelligence of the message. In radio communications, we are
always concerned about bandwidth. If we can get rid of any signal components, we
do not need we can reduce the bandwidth. Reducing bandwidth reduces noise.
Noise is also a component of signals that we can identify far more easily in a digital
frequency domain signal and discard.
Once a signal is converted to the frequency domain and digitised, now a discrete
signal, we can use computer algorithms in software or hardware to mathematically
manipulate that signal. We can remove noise, reduce bandwidth, apply filtering “as
if” we were using physical filters, and much more.

Fourier transformations make possible JPEG and MP3 compression. Once an
image or sound is discretised in the frequency domain, artifacts, noise and other
components not needed for restoration can be removed. This leads to an automatic
compression. With JPEG and MP3, you can control the amount of artefact removal.
If we go too far with compression, the image or sound suffers distortion, these same
techniques are used in radio communication signals.

When we have finished with mathematical wizardry, the signal can, if necessary, be
converted back to the time domain using an Inverse Fourier Transform. Many
computer programming languages, such as Python, C, and C# etc., have FFT
libraries built into them.

DIGITAL FILTERS

A digital filter is a system that performs mathematical operations on a digital signal
to reduce or modify certain aspects of that signal. This is in contrast to the analogue,
hardware type filter.
A digital filter system comprises of analogue to digital converter (ADC) that samples
the input signal, followed by a microprocessor and memory to store data. Program
instructions (software) running on the microprocessor implement the digital filter by
performing the necessary mathematical operations on the encoded data received
from the ADC. Instead, a microprocessor, or Field Programmable Gate Array
(FPGA) could be used.

PREVIEW
445