Band-stop filter - Wiki(Description)

http://en.wikipedia.org/wiki/Band-stop_filter

Band-stop filter

In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, butattenuates those in a specific range to very low levels. It is the opposite of a band-pass filter. A notch filter is a band-stop filter with a narrow stopband (high Q factor).

Narrow notch filters (optical) are used in Raman spectroscopy, live sound reproduction (public address systems, or PA systems) and in instrument amplifiers (especially amplifiers orpreamplifiers for acoustic instruments such as acoustic guitar,mandolin, bass instrument amplifier, etc.) to reduce or preventaudio feedback, while having little noticeable effect on the rest of the frequency spectrum (electronic or software filters). Other names include 'band limit filter', 'T-notch filter', 'band-elimination filter', and 'band-reject filter'.

Typically, the width of the stopband is 1 to 2 decades (that is, the highest frequency attenuated is 10 to 100 times the lowest frequency attenuated). However, in the audio band, a notch filter has high and low frequencies that may be onlysemitones apart.

Generic electrical schematic of a simple band-stop filter

[hide]

[edit]Examples

[edit]In the audio domain

Anti-hum filter

For countries using 60 Hz power lines:

Low Freq: 59 Hz
High Freq: 61 Hz

This means that the filter passes all frequencies, except for the range of 59–61 Hz. This would be used to filter out themains hum from the 60 Hz power line, though its higher harmonics could still be present.

For countries where power transmission is at 50Hz, the filter would have a 49–51 Hz range.

Anti-presence filter

Low Freq: 1 kHz
High Freq: 4 kHz

For attenuating presence.

[edit]In the radio frequency (RF) domain

Non-linearities of power amplifiers

When measuring the non-linearities of power amplifiers, a very narrow notch filter can be very useful to avoid the carrier frequency. Use of the filter may ensure that the maximum input power of a spectrum analyser used to detect spurious content will not be exceeded.

Wave trap

A notch filter, usually a simple LC circuit, is used to remove a specific interfering frequency. This is a technique used with radio receivers that are so close to a transmitter that it swamps all other signals. The wave trap is used to remove, or greatly reduce, the signal from the local transmitter.^[1]

[edit]In the optical domain

Optical notch filters rely on destructive interference.

Band-pass filter - Wiki(Description)

http://en.wikipedia.org/wiki/Band-pass_filter

Band-pass filter

A band-pass filter is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.

;

Optical band-pass filters are of common usage.

An example of an analogue electronic band-pass filter is an RLC circuit (a resistor–inductor–capacitor circuit). These filters can also be created by combining a low-pass filter with a high-pass filter.^[1]

Bandpass is an adjective that describes a type of filter or filtering process; it is to be distinguished from passband, which refers to the actual portion of affected spectrum. Hence, one might say "A dual bandpass filter has two passbands." A bandpass signal is a signal containing a band of frequencies away from zero frequency, such as a signal that comes out of a bandpass filter.^[2]

An ideal bandpass filter would have a completely flat passband (e.g. with no gain/attenuation throughout) and would completely attenuate all frequencies outside the passband. Additionally, the transition out of the passband would be instantaneous in frequency. In practice, no bandpass filter is ideal. The filter does not attenuate all frequencies outside the desired frequency range completely; in particular, there is a region just outside the intended passband where frequencies are attenuated, but not rejected. This is known as the filter roll-off, and it is usually expressed in dB of attenuation per octave or decade of frequency. Generally, the design of a filter seeks to make the roll-off as narrow as possible, thus allowing the filter to perform as close as possible to its intended design. Often, this is achieved at the expense of pass-band or stop-band ripple.

The bandwidth of the filter is simply the difference between the upper and lower cutoff frequencies. The shape factor is the ratio of bandwidths measured using two different attenuation values to determine the cutoff frequency, e.g., a shape factor of 2:1 at 30/3 dB means the bandwidth measured between frequencies at 30 dB attenuation is twice that measured between frequencies at 3 dB attenuation.

Outside of electronics and signal processing, one example of the use of band-pass filters is in the atmospheric sciences. It is common to band-pass filter recent meteorological data with a period range of, for example, 3 to 10 days, so that onlycyclones remain as fluctuations in the data fields.

In neuroscience, visual cortical simple cells were first shown by David Hubel and Torsten Wiesel to have response properties that resemble Gabor filters, which are band-pass.^[3]

[hide]

[edit]Q-factor

A band-pass filter can be characterised by its Q-factor. The Q-factor is the inverse of the fractional bandwidth. A high-Q filter will have a narrow passband and a low-Q filter will have a wide passband. These are respectively referred to as narrow-band and wide-band filters.

[edit]References in popular culture

The schematic showing "Kilroy", which Pynchon said represents part of a band-pass filter. His drawing actually resembles the schematic of a band-stop filter.

In his first novel, V., Thomas Pynchon quips that the populargraffiti character Kilroy "had sprung into life, in truth, as part of a band-pass filter".^[4]^[5]

High-pass filter - Wiki(Description)

http://en.wikipedia.org/wiki/High-pass_filter

High-pass filter

A high-pass filter (HPF) is an electronic filter that passes high-frequency signals but attenuates (reduces the amplitudeof) signals with frequencies lower than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. A high-pass filter is usually modeled as a linear time-invariant system. It is sometimes called a low-cut filter or bass-cut filter.^[1] High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero average voltages or RF devices. They can also be used in conjunction with a low-pass filter to make a bandpass filter.

[hide]

[edit]First-order continuous-time implementation

Figure 1: A passive, analog, first-order high-pass filter, realized by an RC circuit

The simple first-order electronic high-pass filter shown in Figure 1 is implemented by placing an input voltage across the series combination of a capacitor and aresistor and using the voltage across the resistor as an output. The product of the resistance and capacitance (R×C) is the time constant (τ); it is inversely proportional to the cutoff frequency f_c, that is,

$f_c = \frac{1}{2 \pi \tau} = \frac{1}{2 \pi R C},\,$

where f_c is in hertz, τ is in seconds, R is in ohms, and C is in farads.

Figure 2: An active high-pass filter

Figure 2 shows an active electronic implementation of a first-order high-pass filter using an operational amplifier. In this case, the filter has apassband gain of -R₂/R₁ and has a corner frequency of

$f_c = \frac{1}{2 \pi \tau} = \frac{1}{2 \pi R_1 C},\,$

Because this filter is active, it may have non-unity passband gain. That is, high-frequency signals are inverted and amplified byR₂/R₁.

[edit]Discrete-time realization

For another method of conversion from continuous- to discrete-time, see Bilinear transform.

Discrete-time high-pass filters can also be designed. Discrete-time filter design is beyond the scope of this article; however, a simple example comes from the conversion of the continuous-time high-pass filter above to a discrete-time realization. That is, the continuous-time behavior can be discretized.

From the circuit in Figure 1 above, according to Kirchoff's Laws and the definition of capacitance:

$\begin{cases} V_{\text{out}}(t) = I(t)\, R &\text{(V)}\\ Q_c(t) = C \, \left( V_{\text{in}}(t) - V_{\text{out}}(t) \right) &\text{(Q)}\\ I(t) = \frac{\operatorname{d} Q_c}{\operatorname{d} t} &\text{(I)} \end{cases}$

where $Q_c(t)$ is the charge stored in the capacitor at time $t$ . Substituting Equation (Q) into Equation (I) and then Equation (I) into Equation (V) gives:

$V_{\text{out}}(t) = \overbrace{C \, \left( \frac{\operatorname{d} V_{\text{in}}}{\operatorname{d}t} - \frac{\operatorname{d} V_{\text{out}}}{\operatorname{d}t} \right)}^{I(t)} \, R = R C \, \left( \frac{ \operatorname{d} V_{\text{in}}}{\operatorname{d}t} - \frac{\operatorname{d} V_{\text{out}}}{\operatorname{d}t} \right)$

This equation can be discretized. For simplicity, assume that samples of the input and output are taken at evenly-spaced points in time separated by $\Delta_T$ time. Let the samples of $V_{\text{in}}$ be represented by the sequence $(x_1, x_2, \ldots, x_n)$ , and let $V_{\text{out}}$ be represented by the sequence $(y_1, y_2, \ldots, y_n)$ which correspond to the same points in time. Making these substitutions:

$y_i = R C \, \left( \frac{x_i - x_{i-1}}{\Delta_T} - \frac{y_i - y_{i-1}}{\Delta_T} \right)$

And rearranging terms gives the recurrence relation

$y_i = \overbrace{\frac{RC}{RC + \Delta_T} y_{i-1}}^{\text{Decaying contribution from prior inputs}} + \overbrace{\frac{RC}{RC + \Delta_T} \left( x_i - x_{i-1} \right)}^{\text{Contribution from change in input}}$

That is, this discrete-time implementation of a simple continuous-time RC high-pass filter is

$y_i = \alpha y_{i-1} + \alpha (x_{i} - x_{i-1}) \qquad \text{where} \qquad \alpha \triangleq \frac{RC}{RC + \Delta_T}$

By definition, $0 \leq \alpha \leq 1$ . The expression for parameter $\alpha$ yields the equivalent time constant $RC$ in terms of the sampling period $\Delta_T$ and $\alpha$ :

$RC = \Delta_T \left( \frac{\alpha}{1 - \alpha} \right)$

If $\alpha = 0.5$ , then the $RC$ time constant equal to the sampling period. If $\alpha \ll 0.5$ , then $RC$ is significantly smaller than the sampling interval, and $RC \approx \alpha \Delta_T$ .

[edit]Algorithmic implementation

The filter recurrence relation provides a way to determine the output samples in terms of the input samples and the preceding output. The following pseudocode algorithm will simulate the effect of a high-pass filter on a series of digital samples:

 // Return RC high-pass filter output samples, given input samples,
 // time interval dt, and time constant RC
 function highpass(real[0..n] x, real dt, real RC)
   var real[0..n] y
   var real α := RC / (RC + dt)
   y[0] := x[0]
   for i from 1 to n
     y[i] := α * y[i-1] + α * (x[i] - x[i-1])
   return y

The loop which calculates each of the $n$ outputs can be refactored into the equivalent:

   for i from 1 to n
     y[i] := α * (y[i-1] + x[i] - x[i-1])

However, the earlier form shows how the parameter α changes the impact of the prior output y[i-1] and current changein input (x[i] - x[i-1]). In particular,

A large α implies that the output will decay very slowly but will also be strongly influenced by even small changes in input. By the relationship between parameter α and time constant $RC$ above, a large α corresponds to a large $RC$ and therefore a low corner frequency of the filter. Hence, this case corresponds to a high-pass filter with a very narrow stop band. Because it is excited by small changes and tends to hold its prior output values for a long time, it can pass relatively low frequencies. However, a constant input (i.e., an input with (x[i] - x[i-1])=0) will always decay to zero, as would be expected with a high-pass filter with a large $RC$ .
A small α implies that the output will decay quickly and will require large changes in the input (i.e., (x[i] - x[i-1]) is large) to cause the output to change much. By the relationship between parameter α and time constant $RC$ above, a small α corresponds to a small $RC$ and therefore a high corner frequency of the filter. Hence, this case corresponds to a high-pass filter with a very wide stop band. Because it requires large (i.e., fast) changes and tends to quickly forget its prior output values, it can only pass relatively high frequencies, as would be expected with a high-pass filter with a small $RC$ .

[edit]Applications

[edit]Audio

High-pass filters have many applications. They are used as part of an audio crossover to direct high frequencies to atweeter while attenuating bass signals which could interfere with, or damage, the speaker. When such a filter is built into aloudspeaker cabinet it is normally a passive filter that also includes a low-pass filter for the woofer and so often employs both a capacitor and inductor (although very simple high-pass filters for tweeters can consist of a series capacitor and nothing else). As an example, the formula above, applied to a tweeter with R=10 Ohm, will determine the capacitor value for a cut-off frequency of 5 KHz. $C = \frac{1}{2 \pi f R} = \frac{1}{6.28 * 5000 * 10} = 3.18 * 10^{-6}$ , or approx 3.2 μF.

An alternative, which provides good quality sound without inductors (which are prone to parasitic coupling, are expensive, and may have significant internal resistance) is to employ bi-amplification with active RC filters or active digital filters with separate power amplifiers for each loudspeaker. Such low-current and low-voltage line level crossovers are called active crossovers.^[1]

Rumble filters are high-pass filters applied to the removal of unwanted sounds near to the lower end of the audible range or below. For example, noises (e.g., footsteps, or motor noises from record players and tape decks) may be removed because they are undesired or may overload the RIAA equalization circuit of the preamp.^[1]

High-pass filters are also used for AC coupling at the inputs of many audio power amplifiers, for preventing the amplification of DC currents which may harm the amplifier, rob the amplifier of headroom, and generate waste heat at the loudspeakers voice coil. One amplifier, the professional audio model DC300 made by Crown International beginning in the 1960s, did not have high-pass filtering at all, and could be used to amplify the DC signal of a common 9-volt battery at the input to supply 18 volts DC in an emergency for mixing console power.^[2] However, that model's basic design has been superseded by newer designs such as the Crown Macro-Tech series developed in the late 1980s which included 10 Hz high-pass filtering on the inputs and switchable 35 Hz high-pass filtering on the outputs.^[3] Another example is the QSC Audio PLX amplifier series which includes an internal 5 Hz high-pass filter which is applied to the inputs whenever the optional 50 and 30 Hz high-pass filters are turned off.^[4]

A 75 Hz "low cut" filter from an input channel of a Mackie 1402 mixing console as measured by Smaart software. This high-pass filter has a slope of 18 dB per octave.

Mixing consoles often include high-pass filtering at each channel strip. Some models have fixed-slope, fixed-frequency high-pass filters at 80 or 100 Hz that can be engaged; other models have 'sweepable HPF'—a high-pass filter of fixed slope that can be set within a specified frequency range, such as from 20 to 400 Hz on the Midas Heritage 3000, or 20 to 20,000 Hz on the Yamaha M7CL digital mixing console. Veteran systems engineer and live sound mixer Bruce Main recommends that high-pass filters be engaged for most mixer input sources, except for those such as kick drum, bass guitar and piano, sources which will have useful low frequency sounds. Main writes that DI unit inputs (as opposed to microphone inputs) do not need high-pass filtering as they are not subject to modulation by low-frequency stage wash—low frequency sounds coming from the subwoofers or the public address system and wrapping around to the stage. Main indicates that high-pass filters are commonly used for directional microphones which have a proximity effect—a low-frequency boost for very close sources. This low frequency boost commonly causes problems up to 200 or 300 Hz, but Main notes that he has seen microphones that benefit from a 500 Hz HPF setting on the console.^[5]

[edit]Image

Example of high-pass filter applied to the right half of a photograph. Left side is unmodified, Right side is with a high-pass filter applied (in this case, with a radius of 4.9)

High-pass and low-pass filters are also used in digital image processing to perform image modifications, enhancements, noise reduction, etc., using designs done in either the spatial domain or the frequency domain.^[6]

A high-pass filter, if the imaging software does not have one, can be done by duplicating the layer, putting a gaussian blur, inverting, and then blending with the original layer using an opacity (say 50%) with the original layer. ^[7]

The unsharp masking, or sharpening, operation used in image editing software is a high-boost filter, a generalization of high-pass.

Jana

Saturday, 12 January 2013

Band-stop filter - Wiki(Description)

Band-stop filter

Contents

[edit]Examples

[edit]In the audio domain

[edit]In the radio frequency (RF) domain

[edit]In the optical domain

Band-pass filter - Wiki(Description)

Band-pass filter

Contents

[edit]Q-factor

[edit]References in popular culture

High-pass filter - Wiki(Description)

High-pass filter

Contents

[edit]First-order continuous-time implementation

[edit]Discrete-time realization

[edit]Algorithmic implementation

[edit]Applications

[edit]Audio

[edit]Image