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# Accession Number:

## AD0656611

# Title:

## TIME DOMAIN ANALYSIS OF IMPULSE RESPONSE TRAINS.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS

# Report Date:

## 1967-05-31

# Pagination or Media Count:

##
73.0

# Abstract:

## An impulse response train is a signal that can be described as the response of a linear time-invariant system to a sequence of equally spaced impulses of varying areas. The impulse response associated with such a signal is called the kernel of the impulse response train. A variety of physical systems generate signals in a manner indicating that the signals can be modeled by impulse response trains. Examples of such signals are the voiced sounds of speech, and the individual tones of wind instruments. Knowledge of the kernel of such physically generated signals would be useful for two reasons. First, the physical generating system can be simulated by a linear time-invariant system with the kernel as impulse response. Second, the class of signals generated by the system can be characterized by the kernel. This report shows how to find the kernel of an impulse response train directly from the signal itself. The method used to find the kernel involves only matrix multiplication and the solving of simultaneous linear equations. Once the kernel is found, the impulse areas can be determined, again, by the solution of simultaneous linear equations. All of these operations can be routinely carried out by an electronic digital computer.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#