What is an Anti-Aliasing Filter?

An anti-aliasing filter is a filter placed before a signal is sampled by an analog-to-digital converter (ADC) to remove frequencies that are too high to be represented correctly after sampling.

Why it is needed

When converting a continuous signal into digital samples, the sampling rate limits the highest frequency that can be represented. This limit is defined by the Nyquist–Shannon Sampling Theorem.

• If the sampling rate is Fs, the highest recoverable frequency is Fs / 2 (the Nyquist frequency).
• Any signal component above Fs/2 will appear falsely as a lower frequency after sampling.
• This distortion is called Aliasing.

The anti-aliasing filter removes those high-frequency components before sampling, preventing them from folding into the measured spectrum.

What the filter usually is

Most commonly it is a low-pass filter:

• Passband: desired signal frequencies
• Stopband: frequencies above the Nyquist frequency

Example:

The cutoff is set slightly below Nyquist to allow the filter to roll off.

Simple diagram

Analog signal
      │
      ▼
Anti-Aliasing Filter (Low-Pass)
      │
      ▼
ADC (Sampling)
      │
      ▼
Digital Signal

Real-world examples

Anti-aliasing filters are used in:

• Digital audio recording (before ADC in microphones or audio interfaces)
• Software defined radio receivers
• Oscilloscopes
• Image sensors (optical low-pass filters in cameras)
• Scientific instruments

Example in radio astronomy

If a receiver samples at 2 MHz, any signals above 1 MHz baseband must be suppressed. Otherwise strong RFI above that frequency could alias into the band of interest and appear as false spectral lines.

ANTI-ALIASING FILTER

An anti-aliasing filter is a filter placed before an Analog-to-Digital Converter (ADC).
Its purpose is to remove signal frequencies that are too high to be correctly represented after sampling.

If those high frequencies are not removed, they appear as incorrect lower frequencies in the digital data.
This effect is called aliasing.

1. Why aliasing happens

When a signal is sampled, the sampling rate limits the highest frequency that can be measured correctly.

Nyquist frequency = Fs / 2

where

Fs = sampling rate

Example

Sampling rate Fs = 2 MHz

Nyquist frequency = 1 MHz

Any signal above 1 MHz will appear at the wrong frequency after sampling.

Example of aliasing

Sampling rate = 2 MHz
Nyquist frequency = 1 MHz

Suppose a signal exists at 1.3 MHz.

Aliased frequency can be calculated as

f_alias = | f_signal – n * Fs |

Choose n = 1

f_alias = | 1.3 – 2.0 |

f_alias = 0.7 MHz

So a signal at 1.3 MHz appears in the spectrum at 700 kHz.

What the spectrum would look like

Actual signal:

1.3 MHz (outside the observable band)

Observed spectrum after sampling:

0 Hz ———————- 1 MHz * 700 kHz (false signal)

This false signal is the alias.

2. Purpose of the anti-aliasing filter

The anti-aliasing filter removes frequencies above the Nyquist frequency before the ADC samples the signal.

Signal chain:

Analog Signal | V Anti-Aliasing Filter (Low Pass) | V ADC | V Digital Signal

3. Example for an SDR receiver

Suppose:

Sample rate = 2 MHz
Nyquist frequency = 1 MHz

We want to observe frequencies from

0 Hz to 900 kHz

The anti-aliasing filter should therefore suppress frequencies above about 1 MHz.

Target:

0 – 900 kHz pass band

1 MHz strongly attenuated

4. Simple RC anti-alias filter

Cutoff frequency formula

fc = 1 / (2 * pi * R * C)

Example

R = 180 ohms
C = 1 nF

fc approx 884 kHz

However, a single RC filter only rolls off slowly (6 dB per octave), so strong interference may still leak through.

5. Better solution

Most receivers use higher order filters such as

Butterworth low-pass filter

Typical design

Order: 4 to 6
Cutoff: about 0.9 * Nyquist frequency

Advantages

• flat passband
• steep attenuation above cutoff
• much better rejection of unwanted signals

6. Typical receiver chain in radio astronomy

Antenna | LNA (low noise amplifier) | RF bandpass filter | Mixer or downconverter | Anti-alias low-pass filter | ADC or SDR

7. Why this matters in radio astronomy

Without an anti-aliasing filter:

• strong transmitters outside the band
• can fold into the observed spectrum
• appear as false spectral lines
• corrupt long integrations

This is particularly important when observing weak signals such as the 1420 MHz hydrogen line.

ANTI-ALIAS FILTER DESIGN FOR A 1420 MHz SDR RECEIVER

In hydrogen line radio astronomy the receiver usually converts
1420.405 MHz down to baseband before sampling.

Example receiver parameters:

RF frequency = 1420.405 MHz
Sample rate (Fs) = 2 MHz
Nyquist frequency = Fs / 2 = 1 MHz

Therefore only frequencies between

0 Hz and 1 MHz

can be represented correctly.

To avoid aliasing we normally design the anti-alias filter slightly below Nyquist.

Typical design target:

Passband : 0 to 900 kHz
Stopband : above 1 MHz

Example simple LC low-pass filter (3 pole)

            L1            L2

Input —-coil—-+—-coil—-+—- Output | | C1 C2 | | GND GND

Example component values for about 900 kHz cutoff:

L1 = 22 uH
L2 = 22 uH
C1 = 1.2 nF
C2 = 1.2 nF

Characteristics:

Passband: flat to about 800 to 900 kHz
Rolloff : about 18 dB per octave

For stronger RFI rejection, a 5 pole filter is better.

Example 5 pole low-pass filter

Input –L1–+–L2–+–L3– Output | | | C1 C2 C3 | | | GND GND GND

Typical values for about 900 kHz cutoff:

L1 = 18 uH
L2 = 27 uH
L3 = 18 uH

C1 = 1.5 nF
C2 = 2.2 nF
C3 = 1.5 nF

This gives much better suppression near Nyquist.

Typical SDR receiver chain

Antenna | V LNA | V RF Bandpass Filter (around 1420 MHz) | V Mixer / Downconverter | V Anti-Alias Low Pass Filter (about 900 kHz cutoff) | V ADC / SDR

TABLE OF ALIAS FREQUENCIES

This table shows where signals above Nyquist appear in the spectrum.

Example sample rate:

Fs = 2 MHz
Nyquist = 1 MHz

Real Frequency Observed Frequency

1.1 MHz 0.9 MHz
1.2 MHz 0.8 MHz
1.3 MHz 0.7 MHz
1.4 MHz 0.6 MHz
1.5 MHz 0.5 MHz
1.6 MHz 0.4 MHz
1.7 MHz 0.3 MHz
1.8 MHz 0.2 MHz
1.9 MHz 0.1 MHz

ASCII visualization

Real spectrum (before sampling)

0 —-1 MHz—-2 MHz | real signal 1.3 MHz

Observed spectrum (after sampling)

0 ———–1 MHz * 700 kHz

The signal has “folded” around the Nyquist frequency.

Quick rule for alias frequency

alias = abs( signal_frequency – n * sample_rate )

where n is an integer chosen so the result falls inside the sampled band.

Why this matters for hydrogen line work

If strong signals exist near the receiver, for example

mobile transmitters
satellites
radar

they may enter the receiver above the Nyquist frequency and appear as false narrow lines in the spectrum.

Without an anti-alias filter these signals can look very similar to real astronomical spectral features.