The Sampling Theorem states that a continuous signal can be completely represented by its samples if the sampling frequency is at least twice the highest frequency of the signal, also known as the Nyquist rate.
It is a principle that allows the reconstruction of a signal by using a limited number of its samples.
The theorem that states maximum signal amplitude is given by the peak value of its samples.
A theorem that describes the minimum bandwidth required for an error-free transmission.
It was formulated by Joseph Fourier in 1822.
Formulated by Harry Nyquist in 1924.
The Sampling Theorem was formulated by Claude Shannon in 1949, although it was prefigured by Harry Nyquist and others earlier.
Formulated by John Von Neumann in 1945.
It is a unit of measure for signal-to-noise ratio.
The rate at which a signal can be transmitted over a channel.
The Nyquist rate is the minimum sampling rate required to avoid aliasing, equal to twice the highest frequency present in the signal.
The rate of increase in frequency components over time.
Aliasing is the phenomenon that occurs when a signal is sampled below the Nyquist rate, causing different signal frequencies to become indistinguishable or 'aliased' in the sampled data.
Aliasing refers to the improvement of signal clarity through advanced sampling.
Aliasing occurs when a signal is perfectly reconstructed from its samples.
It is a method of encoding digital signals efficiently.
By increasing the bandwidth of the sampling equipment.
Aliasing can be prevented by using a low-pass filter to remove frequencies higher than half the sampling rate before sampling the signal.
By decreasing the amplitude of the input signal.
Through the use of higher resolution signal converters.
The Nyquist frequency is half the sampling rate of a discrete signal processing system and represents the highest frequency that can be accurately represented.
It refers to the frequency at which a signal changes phases.
The Nyquist frequency determines the minimum energy required for a signal to be sampled.
A frequency that indicates a peak in signal noise.
The Sampling Theorem is crucial because it provides the foundation for converting continuous signals to discrete form without loss of information, which is essential for digital processing and storage.
It allows signals to be processed at arbitrary speeds.
Because it allows the reduction of signal amplitude without distortion.
It ensures that signals can be transmitted in multiple formats simultaneously.
Over-sampling is a technique used to predict future signal values.
It refers to sampling that fails to represent the signal accurately due to a low rate.
Over-sampling occurs when a signal is sampled at a rate significantly higher than the Nyquist rate, which can be used to improve signal resolution and reduce noise.
Over-sampling is when a signal is sampled exactly at the Nyquist rate.
The components are automatically filtered out during sampling.
Frequency components beyond the Nyquist limit cause aliasing in the sampled signal, which distorts the original signal’s representation.
The signal remains unaffected and easily reconstructable.
It increases the overall amplitude of the sampled signal.
By using complex algorithms to simulate frequency components.
By reducing the sampling rate to fit storage requirements.
In practice, the Nyquist criterion is applied by ensuring sampling rates are set above the Nyquist rate and by using anti-aliasing filters to remove high-frequency noise.
Through the direct amplification of signal currents.
Yes, the Sampling Theorem can be applied to non-periodic signals by considering the signal’s bandwidth and ensuring the sampling rate is twice the signal's maximum frequency component.
No, the Sampling Theorem is strictly for periodic signals.
It can only be applied if the non-periodic signals are first converted into periodic forms.
Yes, but only with the use of specialized adaptive filters.
A practical example is the digital audio player, which uses the Sampling Theorem to convert analog audio signals into digital form accurately.
A purely analog broadcasting system.
Mechanical watches measuring acoustic vibrations.
Traditional pneumatic systems without digital control.
Quantization is the process of mapping a continuous range of values (such as a sample of an analog signal) to a finite range of discrete levels.
A process in which signals are continuously monitored at high frequencies.
An algorithm design technique for signal repair.
A method of increasing the amplitude of a digital signal.
The Sampling Theorem allows telecommunications systems to efficiently encode continuous signals into digital signals, which are more robust for transmission over long distances.
It is used to synchronize broadcasting equipment in separate locations.
The theorem helps compress voice signals in cellphones to save bandwidth.
It is central to designing analog antennas for various frequencies.
A band-limited signal only affects one particular frequency band during transmission.
Band-limited signals cannot be sampled according to the Sampling Theorem.
A band-limited signal is one that contains no frequency components higher than a certain cutoff frequency, which ensures that it can be sampled without aliasing if the sampling rate meets the Nyquist criterion.
Band-limited signals exceed the Nyquist rate, causing unavoidable aliasing.