The normally risky situation of having a filter pole directly on the z-plane's unit circle need not trouble us here because there can be no coefficient quantization error in our H cic( z) transfer function. , D–1, corresponding to a magnitude null in Figure 5(a). Each of the comb's zeros, being a Dth root of 1, are located at z( m) = e j 2 p m / D, where m = 0, 1, 2.
(This is why CIC filters are sometimes called sinc filters.)ĭigital filter designers like to see z-plane pole/zero plots, so I provide the z-plane characteristics of a D = 5 CIC filter in Figure 5(C), where the comb filter produces D zeros, equally spaced around the unit-circle, and the integrator produces a single pole canceling the zero at z = 1. This means the CIC filter's frequency magnitude response is approximately equal to a sin( x)/ x function centered at 0 Hz as we see in Figure 5(a). (8), that ratio of sin() terms can be approximated by a sin( x)/ x function. The D-point moving-average filter's time-domain output is expressed as There we see that D–1 summations (plus one multiply by 1/ D) are necessary to compute the averager's y( n) output sequence.įigure 2: D -point moving-average and recursive running sum filters. Recall the standard D-point moving-average process in Figure 2(a). With that said, let's see how CIC filters operate.ĬIC filters originate from the notion of a recursive running sum filter, which is itself an efficient form of a nonrecursive moving averager. * Narrowband lowpass filtering can be attained at a greatly reduced computational complexity compared to using a single lowpass FIR filter. And this property is why CIC filters are so attractive in decimating and interpolating DSP systems. The arithmetic needed to implement CIC filters is strictly additions and subtractions only. * CIC filters are popular in hardware devices they need no filter coefficient data storage and require no multiplications. * The FIR filters operate at reduced clock rates minimizing power consumption in high-speed hardware applications The Figure 1 cascaded-filter architectures have valuable benefits. Both applications are associated with very high-data rate filtering such as hardware quadrature modulation and demodulation in modern wireless systems, and delta-sigma A/D and D/A converters.įigure 1: CIC filter applications: (a) for decimation (b) for interpolation.īecause their frequency magnitude responses are sin( x)/ x-like, CIC filters are typically followed, or preceded, by linear-phase lowpass tapped-delay line finite impulse response (FIR) filters whose tasks are to compensate for the CIC filter's non-flat passband. Hailing from East Flatbush, Brooklyn and one of the breakout stars of the Brooklyn Drill hip-hop scene, Sleepy Hallow came to prominence in 2020 with the RIAA Gold-certified hit “Deep End Freestyle” which featured vocals by Fousheé. Recently selected as one of HipHopDX Rising Stars 2021 and BET Amplified Artist of the Month (January), Hallow’s impressive repertoire of EPs.This article is available in PDF format for easy printingĪfter describing a few applications of CIC filters, this blog introduces their structure and behavior, presents the frequency-domain performance of CIC filters, and discusses several important practical issues in implementing these filters.ĬIC filters are well-suited for anti-aliasing filtering prior to decimation (sample rate reduction), as shown in Figure 1(a) and for anti-imaging filtering for interpolated signals (sample rate increase) as in Figure 1(b). Sleepy transforms his relatively lowkey persona on each of the 14 tracks with hard-hitting lyrics, signifying to the masses to not sleep on his undeniable skills. Still Sleep? will include previously released tracks “2 Sauce” and “2055,” which gave listeners a preview of what’s to come on the Great John-produced album. The album is currently available for pre-save and pre-order at various digital service providers. Winners Circle Wednesdays continues with the release of two new tracks and video by Sleepy Hallow – “ Chicken ” and “ Mi No Sabe.” The singles and video delivers more heat for the highly anticipated release of Sleepy Hallow’s debut album Still Sleep? on June 2 via Winners Circle Entertainment/RCA Records.