Time Domain

Time domain is a term used to describe the analysis of:

·         mathematical functions,

·         physical signals or time series of economic or environmental data, with respect to time.

In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various separate instants in the case of discrete time.

Tool used to visualize real-world signals in the time domain is oscilloscope.

Time domain graph shows how a signal changes over time, whereas a frequency domain graph shows how much of the signal lies within each given frequency band over a range of frequencies.

The simple manipulation of a signal's time-domain representation is waveform and it can provide a number of useful properties.

Visualization of periodic, aperiodic, and swept-frequency waveforms.

Visualizing a speech signal in the time domain using the Signal Browser interface in the Signal Processing Tool (SPTool).

The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Digital filtering generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal. There are various ways to characterize filters; for example:

§  A "linear" filter is a linear transformation of input samples; other filters are "non-linear". Linear filters satisfy the superposition condition, i.e. if an input is a weighted linear combination of different signals, the output is an equally weighted linear combination of the corresponding output signals.

§  A "causal" filter uses only previous samples of the input or output signals; while a "non-causal" filter uses future input samples. A non-causal filter can usually be changed into a causal filter by adding a delay to it.

§  A "time-invariant" filter has constant properties over time; other filters such as adaptive filters change in time.

§  A "stable" filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An "unstable" filter can produce an output that grows without bounds, with bounded or even zero input.

§  A "finite impulse response" (FIR) filter uses only the input signals, while an "infinite impulse response" filter (IIR) uses both the input signal and previous samples of the output signal. FIR filters are always stable, while IIR filters may be unstable.

Filters can be represented by block diagrams, which can then be used to derive a sample processing algorithm to implement the filter with hardware instructions. A filter may also be described as a difference equation, a collection of zeroes and poles or, if it is an FIR filter, an impulse response orstep response.

The output of a digital filter to any given input may be calculated by convolving the input signal with the impulse response.