Remember, for most passband filters, the magnitude response typically varies by up to 3 dB within the passband. This is a common characteristic and is considered an industry standard.
The term '-3dB frequency response' is used frequently to indicate that power has decreased to 50% of its maximum or original amount. However, it also states that the signal voltages have reduced to 0.707 of their highest value. So,
The -3dB comes from either 10 Log (0.5) {in the case of signal's power}
or 20 Log (0.707) {{in the case of signal's amplitude}
Viewing the signal in the frequency domain is quite helpful. In electronic amplifiers, the +/-3dB limit is commonly utilized. It makes it clear whether or not the signal is a flat pass-band. You can observe that the signal in the case of pulse shaping is nearly flat along +/-3dB bandwidth.
The phrase "+/-3 dB" originally meant flatness in the above figure, not high- and low-frequency extension. For instance, one could state that "between 100 Hz and 18 kHz, the signal is flat, within +/-3 dB." Accordingly, a device's frequency response graph (i.e., for speakers) would not depart from a straight line between two frequencies by more than 3 dB in either direction.
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. - - - - - - - - - - - . Filters
Particularly in communication applications, continuous gain over a wider bandwidth is necessary. The difference in frequencies between +/-3 dB values is what constitutes the bandpass filter's bandwidth. Growth reasonably stays consistent in this area. Beyond the 3dB barrier, attenuation is significant, increasing the likelihood of information loss. Therefore, when the voltage is reduced from maximum to 0.707Max, or the power is reduced from maximum to half power, the signal's bandwidth is determined.
In signal processing, maintaining the integrity of the signal within the passband is critical. A signal that drops to less than 50% of its original (maximum) power—equivalent to a 3 dB reduction—is generally considered unacceptable. This threshold is based on the standard that the passband of a filter should preserve most of the signal's energy. If the signal power falls below this level within the passband after filtering, it indicates excessive attenuation, which can lead to significant distortion or loss of important information. Such behavior is typically unacceptable in many practical applications, especially in audio signal processing, where fidelity and clarity are essential. Therefore, a well-designed filter ensures that the variation in magnitude response within the passband remains within a 3 dB tolerance to maintain signal quality.
Application of -3dB Frequency Response
All sorts of filters frequently employ the -3dB point (low pass, band pass, high pass...). It only states that the filter only allows half of the power at that frequency to pass.
In the case of digital filter designing, we often use a bandpass filter to pass frequency components that fall in a particular range (e.g., frequencies that fall between h1 to h2 Hz). Here, the bandpass filter will allow the passing of the frequencies, which range from h1 to h2 Hz; other frequencies will be discarded. The signal is called a flat passband if the magnitude in this frequency range doesn't vary much. In most cases, for filters, it varies between +/- 3db in magnitude.
Why Signal Amplitude Reduces After Bandpass Filtering
In real-world filters, the amplitude of a signal is often scaled due to unity energy normalization, which is applied to preserve the total signal power. This normalization ensures that the filtered signal maintains the same power as the original but results in a reduction in amplitude.
1. Signal Power Before Filtering
For a sinusoidal signal:
The power P_x of the signal is given by:
2. Bandpass Filter and Unity Energy Normalization
A bandpass filter with a constant gain H(f) over the passband ensures power normalization by scaling the gain such that:
For a filter with bandwidth B = f₂ - f₁, the gain is:
The filter scales the signal by 1/√B to normalize the power.
3. Effect on Signal Amplitude
After filtering, the power of the filtered signal is the same as the original, but the amplitude is reduced. For sinusoidal signals:
The amplitude of the filtered signal Ay is scaled as:
4. Example: Amplitude Halving
Consider a sinusoidal signal:
If the filter has a bandwidth B = 2, the amplitude of the filtered signal becomes:
Thus, the amplitude is reduced by approximately 29.3%.
If filter bandwidth B = 4, then the amplitude of the filtered signal reduces to 50%, and so on.
5. Why This Happens
Real-world filters are designed to prioritize power preservation rather than amplitude. This normalization ensures the filter does not artificially boost or reduce the signal's power.
Read also about
- MATLAB Code for understanding +/- 3 dB Frequency Response of a Bandpass Filter
- Filters
- Online Digital Filter Simulator