ERRORSERRORS IN IN

ANALOG SIGNAL ANALOG SIGNAL PROCESSINGPROCESSING

ERROR: Discrepancy between a system’s actual output and its ideal output is called error.

ABSOLUTE ERROR : This error e is the difference between actual value and the ideal value for a quantity.

e= Actual value –Ideal value

RELATIVE ERROR : The relative error є is the quotient between the absolute error and ideal value

Є = e / Ideal value

CLASSIFICATION OF ERRORSCLASSIFICATION OF ERRORS

For Complex Quantities such as Impedance or

Transfer Function there three defined errors :-Vector Error:- Actual Vector – Ideal Vector

Magnitude Error :-Actual Modulus – Ideal modulus

Phase Error :- Actual Phase angle-Ideal Phase angle

Zero Errors:- Errors whose magnitude is independent of actual system input.

Gain Errors:- Errors whose magnitude is proportional to actual system input

Nonlinear Errors :-Errors that depends on actual System input but are not proportional to it.

Systematic Errors

A systematic error is any error that , when applying the same input to the system in same conditions ,remains constant in magnitude and sign or varies according to a definite law.

Temperature ,Aging of system and Power supply are relevant condition that affect system response.

SYSTEM CALIBRATION: A process in which we apply well known input series to system for detection of systematic error.

To avoid systematic errors system must be calibrated very often

Random ErrorsRandom Errors

Appear when same input is repeatedly applied to a system.

Output will seldom be the same if measured with a resolution high enough.

If only gaussian-distributed random error is present, the arithmetic mean of random error for a large number of readings will be zero.

Random ErrorsRandom Errors

Therefore actual system output can be calculated by taking the average of a set of output reading.

For a given system working under specified environmental condition, random error do not exceed a fixed value.

Random error results from the contribution of several independent factors to the system output, none of which dominates over other.

Static ErrorStatic Error

Appear when the system input signal has a very low frequency(<0.01Hz).

These error can be zero, gain or nonlinearity error and systematic or random error.

In analog signal processing, zero errors are termed as offset errors and have a systematic component and a random componenet.

Dynamic ErrorDynamic Error

It is the difference between the actual system output and the ideal output when static error is zero.

It describe the different behavior of the system for the same input amplitude depending on whether this is almost constant (static response)or change with time(dynamic response).

When fast signal is applied to a system, output can be separated into two: transient response and steady-state response.

Dynamic ErrorDynamic Error

The transient stage lasts from the moment the input has been applied to the moment when the output reaches its final value.

Error in the transient stage are termed transient errors.

The steady-state stage starts when the transient response has died out.

Error in steady-state stage is termed as steady-state errors.

Dynamic ErrorDynamic Error

Both transient errors and steady-state errors are dynamic errors.

Dynamic error can be additive, multiplicative and nonlinear errors.

For transient signal(step, ramp), transient error are consider and for periodic signals, steady-state error are consider.