Sampling a Digital Signal

sampling by integer factor L

2

bottom plot range

50

sampler

up

down

Sampling data is the first step in the signal processing of wave forms coming from radar, submarine detection, earthquakes, seismic oil exploration, etc. Up-sampling and down-sampling are the basic operations in multirate discrete-time systems.

The bottom part of the figure shows up-sampling and down-sampling by an integer factor

L>1

of the signal at the top. For the up-sampling process,

L-1

equidistant zero-valued samples are inserted by the up-sampler between each consecutive sample of the input sequence

x(n)

.

Conversely, the down-sampling operation on the input sequence consists of keeping every

th

L

sample of

x(n)

and removing the others.

Details

The up-sampled sequence

y(n)

is developed according to the input sequence

x(n)

:

y(n)=

x(n/L)	n=0,±L,±2L,…,
0	otherwise

The sampling rate of

y(n)

is

L

times larger than that of the original sequence

x(n)

.

The down-sampled sequence

y(n)

is developed according to the input sequence

x(n)

:

y(n)=x(nL)

Here the sampling rate of

y(n)

is

th

1

L

that of the original sequence

x(n)

.

S. Mitra, Digital Signal Processing, 3rd ed., New York: McGraw-Hill, 2005.

External Links

Nyquist Frequency (Wolfram MathWorld)

Oversampling (Wolfram MathWorld)

Permanent Citation

Siva Perla

"Sampling a Digital Signal"
http://demonstrations.wolfram.com/SamplingADigitalSignal/
Wolfram Demonstrations Project
Published: September 28, 2007