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Yes anti-alias filtering is always necessary unless you are convinced there is no spectral energy in the frequencies that would otherwise alias in to the primary spectrum used including and importantly the noise floor itself. (Unless we are not concerned with achieving the full sensitivity as limited by the ADC itself). Typically the primary spectrum is within the frequency for $-f_s/2$ to $+f_s/2$ and frequencies outside of this range can alias in, but a higher frequency band that is $N f_s/2$ to $(N+1) f_s/2$ can also be selected (bandpass sampling).

If a signal is intermittent, but has energy in folding zones intermittently, then that energy will intermittently fold into the primary spectrum if it lands on the frequency regions that would alias in.

Here are some graphics to help understand what is happening and why anti-alias filtering is required:

The first graphic shows the frequency spectrums involved in sampling a 3 Hz Sine wave with a 20 Hz sampling clock.

The top spectrum is the analog spectrum showing the Fourier Transform of a 3 Hz sine wave as two impulses in the frequency domain at +/- 3 Hz.

The middle spectrum shows the spectrum of the sampling process. Sampling in time is multiplying the analog waveform with a train of impulses. The Fourier Transform of a train of impulses in the time domain is a train of impulses in the frequency domain (we see a DC term, the 20 Hz sampling clock, and all the higher harmonics).

The bottom plot shows the digital spectrum that results as the convolution in frequency of the top two spectrums (multiplying in time is convolution in frequency). The convolution with impulses simply creates a copy of the analog spectrum wherever the spectrum appears in the Sampling Process spectrum. This results in the spectrum from $-f_s/2$ to $+f_s/2$ (First Nyquist Zone) being replicated in all higher Nyquist Zones. And for this reason we typically only need to show the digital spectrum from $-f_s/2$ to $+f_s/2$ as the rest is redundant. However visualizing this periodic spectrum extended to infinity can be helpful in understanding mixed signal (analog and digital) concepts. A key point to take away from this is the digital spectrum is periodic. What is in the first Nyquist Zone in the Digital Sepctrum must also be in the higher Nyquist Zones. Similarly anything introduced into the higher Nyquist Zones MUST be in the first Nyquist Zone (they are periodically all the same spectrum).

With that all in mind, I will now add another graphic below showing the same thing with an interference signal in the analog spectrum that is in the area of the sampling rate and not filtered with an anti-alias filter. This signal need not be periodic.

The same convolution process described above explains how the higher frequency spectrum aliases into the locations shown, and specifically how it can be an interference within our primary lower frequency spectrum of interest. The higher frequency spectrum must be filtered out prior to sampling to avoid this interference. An anti-alias filter is required.

Even when there is no apparent signals to filter out, the measured noise floor would (should) be amplified prior to sampling with the A/D converter, to be higher than the quantization noise contributions of the A/D, otherwise local quantization noise will dominate SNR degrading the measurement SNR. If an anti-alias filter is omitted, this amplified noise floor that exists in the bands that will alias into our bandwidth of interest will increase the overall noise floor also degrading the measurement SNR. (For the case of a sensitive radio receiver, this would be the receiver noise figure metric that would be significantly effected).

Yes anti-alias filtering is always necessary unless you are convinced there is no spectral energy in the frequencies that would otherwise alias in to the primary spectrum used including and importantly the noise floor itself. (Unless we are not concerned with achieving the full sensitivity as limited by the ADC itself). Typically the primary spectrum is within the frequency for $-f_s/2$ to $+f_s/2$ and frequencies outside of this range can alias in, but a higher frequency band that is $N f_s/2$ to $(N+1) f_s/2$ can also be selected (bandpass sampling).

If a signal is intermittent, but has energy in folding zones intermittently, then that energy will intermittently fold into the primary spectrum if it lands on the frequency regions that would alias in.

Here are some graphics to help understand what is happening and why anti-alias filtering is required:

The first graphic shows the frequency spectrums involved in sampling a 3 Hz Sine wave with a 20 Hz sampling clock.

The top spectrum is the analog spectrum showing the Fourier Transform of a 3 Hz sine wave as two impulses in the frequency domain at +/- 3 Hz.

The middle spectrum shows the spectrum of the sampling process. Sampling in time is multiplying the analog waveform with a train of impulses. The Fourier Transform of a train of impulses in the time domain is a train of impulses in the frequency domain (we see a DC term, the 20 Hz sampling clock, and all the higher harmonics).

The bottom plot shows the digital spectrum that results as the convolution in frequency of the top two spectrums (multiplying in time is convolution in frequency). The convolution with impulses simply creates a copy of the analog spectrum wherever the spectrum appears in the Sampling Process spectrum. This results in the spectrum from $-f_s/2$ to $+f_s/2$ (First Nyquist Zone) being replicated in all higher Nyquist Zones. And for this reason we typically only need to show the digital spectrum from $-f_s/2$ to $+f_s/2$ as the rest is redundant. However visualizing this periodic spectrum extended to infinity can be helpful in understanding mixed signal (analog and digital) concepts. A key point to take away from this is the digital spectrum is periodic. What is in the first Nyquist Zone in the Digital Sepctrum must also be in the higher Nyquist Zones. Similarly anything introduced into the higher Nyquist Zones MUST be in the first Nyquist Zone (they are periodically all the same spectrum).

With that all in mind, I will now add another graphic below showing the same thing with an interference signal in the analog spectrum that is in the area of the sampling rate and not filtered with an anti-alias filter. This signal need not be periodic.

The same convolution process described above explains how the higher frequency spectrum aliases into the locations shown, and specifically how it can be an interference within our primary lower frequency spectrum of interest. The higher frequency spectrum must be filtered out prior to sampling to avoid this interference. An anti-alias filter is required.

Even when there is no apparent signals to filter out, the measured noise floor would (should) be amplified prior to sampling with the A/D converter, to be higher than the quantization noise contributions of the A/D, otherwise local quantization noise will dominate SNR degrading the measurement SNR. If an anti-alias filter is omitted, this amplified noise floor that exists in the bands that will alias into our bandwidth of interest will increase the overall noise floor also degrading the measurement SNR. (For the case of a sensitive radio receiver, this would be the receiver noise figure metric that would be significantly affected).

Yes anti-alias filtering is always necessary unless you are convinced there is no spectral energy in the frequencies that would otherwise alias in to the primary spectrum used. Typically the primary spectrum is within the frequency for $-f_s/2$ to $+f_s/2$ and frequencies outside of this range can alias in, but a higher frequency band that is $N f_s/2$ to $(N+1) f_s/2$ can also be selected (bandpass sampling).

If a signal is intermittent, but has energy in folding zones intermittently, then that energy will intermittently fold into the primary spectrum if it lands on the frequency regions that would alias in.

Here are some graphics to help understand what is happening and why anti-alias filtering is required:

The first graphic shows the frequency spectrums involved in sampling a 3 Hz Sine wave with a 20 Hz sampling clock.

The top spectrum is the analog spectrum showing the Fourier Transform of a 3 Hz sine wave as two impulses in the frequency domain at +/- 3 Hz.

The middle spectrum shows the spectrum of the sampling process. Sampling in time is multiplying the analog waveform with a train of impulses. The Fourier Transform of a train of impulses in the time domain is a train of impulses in the frequency domain (we see a DC term, the 20 Hz sampling clock, and all the higher harmonics).

The bottom plot shows the digital spectrum that results as the convolution in frequency of the top two spectrums (multiplying in time is convolution in frequency). The convolution with impulses simply creates a copy of the analog spectrum wherever the spectrum appears in the Sampling Process spectrum. This results in the spectrum from $-f_s/2$ to $+f_s/2$ (First Nyquist Zone) being replicated in all higher Nyquist Zones. And for this reason we typically only need to show the digital spectrum from $-f_s/2$ to $+f_s/2$ as the rest is redundant. However visualizing this periodic spectrum extended to infinity can be helpful in understanding mixed signal (analog and digital) concepts. A key point to take away from this is the digital spectrum is periodic. What is in the first Nyquist Zone in the Digital Sepctrum must also be in the higher Nyquist Zones. Similarly anything introduced into the higher Nyquist Zones MUST be in the first Nyquist Zone (they are periodically all the same spectrum).

With that all in mind, I will now add another graphic below showing the same thing with an interference signal in the analog spectrum that is in the area of the sampling rate and not filtered with an anti-alias filter. This signal need not be periodic.

The same convolution process described above explains how the higher frequency spectrum aliases into the locations shown, and specifically how it can be an interference within our primary lower frequency spectrum of interest. The higher frequency spectrum must be filtered out prior to sampling to avoid this interference. An anti-alias filter is required.

Even when there is no apparent signals to filter out, the measured noise floor would (should) be amplified prior to sampling with the A/D converter, to be higher than the quantization noise contributions of the A/D, otherwise local quantization noise will dominate SNR degrading the measurement SNR. If an anti-alias filter is omitted, this amplified noise floor that exists in the bands that will alias into our bandwidth of interest will increase the overall noise floor also degrading the measurement SNR. (For the case of a sensitive radio receiver, this would be the receiver noise figure metric that would be significantly effected).

Yes anti-alias filtering is always necessary unless you are convinced there is no spectral energy in the frequencies that would otherwise alias in to the primary spectrum used including and importantly the noise floor itself. (Unless we are not concerned with achieving the full sensitivity as limited by the ADC itself). Typically the primary spectrum is within the frequency for $-f_s/2$ to $+f_s/2$ and frequencies outside of this range can alias in, but a higher frequency band that is $N f_s/2$ to $(N+1) f_s/2$ can also be selected (bandpass sampling).

If a signal is intermittent, but has energy in folding zones intermittently, then that energy will intermittently fold into the primary spectrum if it lands on the frequency regions that would alias in.

Here are some graphics to help understand what is happening and why anti-alias filtering is required:

The first graphic shows the frequency spectrums involved in sampling a 3 Hz Sine wave with a 20 Hz sampling clock.

The top spectrum is the analog spectrum showing the Fourier Transform of a 3 Hz sine wave as two impulses in the frequency domain at +/- 3 Hz.

The middle spectrum shows the spectrum of the sampling process. Sampling in time is multiplying the analog waveform with a train of impulses. The Fourier Transform of a train of impulses in the time domain is a train of impulses in the frequency domain (we see a DC term, the 20 Hz sampling clock, and all the higher harmonics).

The bottom plot shows the digital spectrum that results as the convolution in frequency of the top two spectrums (multiplying in time is convolution in frequency). The convolution with impulses simply creates a copy of the analog spectrum wherever the spectrum appears in the Sampling Process spectrum. This results in the spectrum from $-f_s/2$ to $+f_s/2$ (First Nyquist Zone) being replicated in all higher Nyquist Zones. And for this reason we typically only need to show the digital spectrum from $-f_s/2$ to $+f_s/2$ as the rest is redundant. However visualizing this periodic spectrum extended to infinity can be helpful in understanding mixed signal (analog and digital) concepts. A key point to take away from this is the digital spectrum is periodic. What is in the first Nyquist Zone in the Digital Sepctrum must also be in the higher Nyquist Zones. Similarly anything introduced into the higher Nyquist Zones MUST be in the first Nyquist Zone (they are periodically all the same spectrum).

With that all in mind, I will now add another graphic below showing the same thing with an interference signal in the analog spectrum that is in the area of the sampling rate and not filtered with an anti-alias filter. This signal need not be periodic.

The same convolution process described above explains how the higher frequency spectrum aliases into the locations shown, and specifically how it can be an interference within our primary lower frequency spectrum of interest. The higher frequency spectrum must be filtered out prior to sampling to avoid this interference. An anti-alias filter is required.

Even when there is no apparent signals to filter out, the measured noise floor would (should) be amplified prior to sampling with the A/D converter, to be higher than the quantization noise contributions of the A/D, otherwise local quantization noise will dominate SNR degrading the measurement SNR. If an anti-alias filter is omitted, this amplified noise floor that exists in the bands that will alias into our bandwidth of interest will increase the overall noise floor also degrading the measurement SNR. (For the case of a sensitive radio receiver, this would be the receiver noise figure metric that would be significantly effected).

Yes anti-alias filtering is always necessary unless you are convinced there is no spectral energy in the frequencies that would otherwise alias in to the primary spectrum used. Typically the primary spectrum is within the frequency for $-f_s/2$ to $+f_s/2$ and frequencies outside of this range can alias in, but a higher frequency band that is $N f_s/2$ to $(N+1) f_s/2$ can also be selected (bandpass sampling).

If a signal is intermittent, but has energy in folding zones intermittently, then that energy will intermittently fold into the primary spectrum if it lands on the frequency regions that would alias in.

Here are some graphics to help understand what is happening and why anti-alias filtering is required:

The first graphic shows the frequency spectrums involved in sampling a 3 Hz Sine wave with a 20 Hz sampling clock.

The top spectrum is the analog spectrum showing the Fourier Transform of a 3 Hz sine wave as two impulses in the frequency domain at +/- 3 Hz.

The middle spectrum shows the spectrum of the sampling process. Sampling in time is multiplying the analog waveform with a train of impulses. The Fourier Transform of a train of impulses in the time domain is a train of impulses in the frequency domain (we see a DC term, the 20 Hz sampling clock, and all the higher harmonics).

The bottom plot shows the digital spectrum that results as the convolution in frequency of the top two spectrums (multiplying in time is convolution in frequency). The convolution with impulses simply creates a copy of the analog spectrum wherever the spectrum appears in the Sampling Process spectrum. This results in the spectrum from $-f_s/2$ to $+f_s/2$ (First Nyquist Zone) being replicated in all higher Nyquist Zones. And for this reason we typically only need to show the digital spectrum from $-f_s/2$ to $+f_s/2$ as the rest is redundant. However visualizing this periodic spectrum extended to infinity can be helpful in understanding mixed signal (analog and digital) concepts. A key point to take away from this is the digital spectrum is periodic. What is in the first Nyquist Zone in the Digital Sepctrum must also be in the higher Nyquist Zones. Similarly anything introduced into the higher Nyquist Zones MUST be in the first Nyquist Zone (they are periodically all the same spectrum).

With that all in mind, I will now add another graphic below showing the same thing with an interference signal in the analog spectrum that is in the area of the sampling rate and not filtered with an anti-alias filter. This signal need not be periodic.

The same convolution process described above explains how the higher frequency spectrum aliases into the locations shown, and specifically how it can be an interference within our primary lower frequency spectrum of interest. The higher frequency spectrum must be filtered out prior to sampling to avoid this interference. An anti-alias filter is required.

Even when there is no apparent signals to filter out, the received noise floor would (should) be amplified prior to sampling with the A/D converter, to be higher than the quantization noise contributions of the A/D, otherwise local quantization noise will dominate SNR degrading the receiver "noise figure". If an anti-alias filter is omitted, this amplified noise floor that exists in the bands that will alias into our bandwidth of interest will increase the overall noise floor also significantly degrading the receiver noise figure.

Yes anti-alias filtering is always necessary unless you are convinced there is no spectral energy in the frequencies that would otherwise alias in to the primary spectrum used. Typically the primary spectrum is within the frequency for $-f_s/2$ to $+f_s/2$ and frequencies outside of this range can alias in, but a higher frequency band that is $N f_s/2$ to $(N+1) f_s/2$ can also be selected (bandpass sampling).

If a signal is intermittent, but has energy in folding zones intermittently, then that energy will intermittently fold into the primary spectrum if it lands on the frequency regions that would alias in.

Here are some graphics to help understand what is happening and why anti-alias filtering is required:

The first graphic shows the frequency spectrums involved in sampling a 3 Hz Sine wave with a 20 Hz sampling clock.

The top spectrum is the analog spectrum showing the Fourier Transform of a 3 Hz sine wave as two impulses in the frequency domain at +/- 3 Hz.

The middle spectrum shows the spectrum of the sampling process. Sampling in time is multiplying the analog waveform with a train of impulses. The Fourier Transform of a train of impulses in the time domain is a train of impulses in the frequency domain (we see a DC term, the 20 Hz sampling clock, and all the higher harmonics).

The bottom plot shows the digital spectrum that results as the convolution in frequency of the top two spectrums (multiplying in time is convolution in frequency). The convolution with impulses simply creates a copy of the analog spectrum wherever the spectrum appears in the Sampling Process spectrum. This results in the spectrum from $-f_s/2$ to $+f_s/2$ (First Nyquist Zone) being replicated in all higher Nyquist Zones. And for this reason we typically only need to show the digital spectrum from $-f_s/2$ to $+f_s/2$ as the rest is redundant. However visualizing this periodic spectrum extended to infinity can be helpful in understanding mixed signal (analog and digital) concepts. A key point to take away from this is the digital spectrum is periodic. What is in the first Nyquist Zone in the Digital Sepctrum must also be in the higher Nyquist Zones. Similarly anything introduced into the higher Nyquist Zones MUST be in the first Nyquist Zone (they are periodically all the same spectrum).

With that all in mind, I will now add another graphic below showing the same thing with an interference signal in the analog spectrum that is in the area of the sampling rate and not filtered with an anti-alias filter. This signal need not be periodic.

The same convolution process described above explains how the higher frequency spectrum aliases into the locations shown, and specifically how it can be an interference within our primary lower frequency spectrum of interest. The higher frequency spectrum must be filtered out prior to sampling to avoid this interference. An anti-alias filter is required.

Even when there is no apparent signals to filter out, the measured noise floor would (should) be amplified prior to sampling with the A/D converter, to be higher than the quantization noise contributions of the A/D, otherwise local quantization noise will dominate SNR degrading the measurement SNR. If an anti-alias filter is omitted, this amplified noise floor that exists in the bands that will alias into our bandwidth of interest will increase the overall noise floor also degrading the measurement SNR. (For the case of a sensitive radio receiver, this would be the receiver noise figure metric that would be significantly effected).