Prove that Energy of a power signal is infinite and power of an energy signal is zero.

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written 3.6 years ago by

abhiddongreb864 • 20

• modified 3.6 years ago

1) Let x(t) be the power signal which has finite nonzero power, such that

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The later part of the equation is energy of signal.

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If Energy is finite here, then power would become zero, which is contradictory to the statement we made in the beginnng.

Hence for Power to be finite and nonzero, Energy must be infinite.

2) Let x(t) be the energy signal with Energy E=constant (finite). The power of this signal can be expressed as,

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But here later part of the limit represents signal energy. Hence

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As Energy is finite, and limit tends to infinity into 1/(2T) will result in zero. Hence Power=0

Hence Power of an Energy signal is zero.

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