Hi Can anyone please explain me about Interpolation using FIR filters? I dont understand how they can be used for interpolation. Thanks Anshu

# Interpolation with FIR filters

Started by ●November 22, 2005

Reply by ●November 22, 20052005-11-22

in article 1132685207.779486.257470@o13g2000cwo.googlegroups.com, Anshu at anshu.dhawan@gmail.com wrote on 11/22/2005 13:46:> Can anyone please explain me about Interpolation using FIR filters? I > dont understand how they can be used for interpolation.might you understand how an FIR filter could give you a frequency response that is mostly flat in magnitude and has a mostly linear phase response that represents a delay of half of the FIR length plus a little more (a fraction of a sample time) delay that can been specified in advance? once you get that, then add the concept of "polyphase" (which is just a set of FIR filters, each resulting in a different fractional sample delay) and you got interpolation to the precision of how many polyphase FIR filters in your set. to get even closer, there is the good, old-fashioned linear interpolation (between these finite polyphase filter delays). -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."

Reply by ●November 22, 20052005-11-22

"Anshu" <anshu.dhawan@gmail.com> wrote in message news:1132685207.779486.257470@o13g2000cwo.googlegroups.com...> Hi > > Can anyone please explain me about Interpolation using FIR filters? I > dont understand how they can be used for interpolation.Anshu, Here are some examples for you to consider: Start with a set of samples: [1 2 3 4 3 2 1] Get ready to interpolate them by a factor of 2 by adding zeros where the new samples will occur: [1 0 2 0 3 0 4 0 5 0 4 0 3 0 2 0 1] Now FIR filter this sequence in a few ways: Filter 1: [1 1] Output from Filter 1: [1 1 2 2 3 3 4 4 5 5 4 4 3 3 2 2 1 1] Not a very fancy interpolation; it's just a "hold" function. Filter 2: [0.5 1.0 0.5] Output from Filter 2: [.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5] This one is a little more interesting; it's a linear interpolator. Does that help? Maybe the "trick" is in the zero-stuffing step? Fred

Reply by ●November 23, 20052005-11-23

hi.. I did not understand what the following statements mean...plz explain Filter 1: [1 1] Filter 2: [0.5 1.0 0.5] Fred Marshall wrote:> "Anshu" <anshu.dhawan@gmail.com> wrote in message > news:1132685207.779486.257470@o13g2000cwo.googlegroups.com... > > Hi > > > > Can anyone please explain me about Interpolation using FIR filters? I > > dont understand how they can be used for interpolation. > > Anshu, > > Here are some examples for you to consider: > > Start with a set of samples: > [1 2 3 4 3 2 1] > Get ready to interpolate them by a factor of 2 by adding zeros where the new > samples will occur: > [1 0 2 0 3 0 4 0 5 0 4 0 3 0 2 0 1] > Now FIR filter this sequence in a few ways: > Filter 1: [1 1] > Output from Filter 1: [1 1 2 2 3 3 4 4 5 5 4 4 3 3 2 2 1 1] > Not a very fancy interpolation; it's just a "hold" function. > Filter 2: [0.5 1.0 0.5] > Output from Filter 2: [.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 4.5 4.0 3.5 > 3.0 2.5 2.0 1.5 1.0 0.5] > This one is a little more interesting; it's a linear interpolator. > > Does that help? Maybe the "trick" is in the zero-stuffing step? > > Fred

Reply by ●November 23, 20052005-11-23

"saras" <saras_rajgiri@yahoo.co.in> wrote in message news:1132723963.277636.115240@o13g2000cwo.googlegroups.com...> hi.. > > I did not understand what the following statements mean...plz explain > > Filter 1: [1 1] > Filter 2: [0.5 1.0 0.5]These are the unit sample responses of two filters. Said another way, Filter 1 has an output y(kT)=1.0*x(kT) + 1.0*x(k-1)T Filter 2 has an ouput y(kT)=0.5*x(kT) + 1.0*x(k-1)T + 0.5*x(k-2)T Said another way, The sequences given for the Filters are their coefficients. Fred