Jamie

April 16th, 2010, 04:56 PM

Hey all,

Here is a quick discussion of Smaart v7's MTW vs. Smaart v2-6's FPPO, and includes mention of SIM's standard FFT settings for Transfer Function in the mix. (This inclusion is due to the fact that this post began life as a response to a specific question regarding MTW and how it related to SIM's standard FFT settings for Transfer Function measurements.)

FPPO was our previous version (v2 - v6) of using multiple time windows in Transfer Function to create constant (fractional octave) frequency resolution data. FPPO in fact stands for "24 Fixed Points Per Octave." We achieved this though a devious mixture of FFT size and sample rate (via decimation) choices, as well as some data point banding for good measure (where the raw frequency resolution was much greater than the target 24th octave). SIM II uses a similar process (as does SIM III I believe), but generally relies on a more straight forward process that uses more FFT's with simple decimation (1/2'd sample rates) between each.

The factors that drove SIA's decisions when creating the original SmaartPro FPPO process are many - having as much to do with available processor power and data handling issues as with target resolution and TC's. When we began development of v7, we were able to take a fresh look at FPPO and the FFT settings for Transfer Function measurements. With processor power being what it is today, running FFT's of 16k, 32k or even 64k in real-time was no longer a concern. So we had to ask ourselves, do we need/want to use a multiple FFT based approach? Why not just run a huge FFT and smooth it to whatever target fractional octave resolution we wish?

Our answer for the first question was, yes, we still want to use multiple FFT's as our default. And the reason we do was the answer to the second question. (Here is the quick version) Single 16k and 32k FFTs have measurement TCs (time constants) of 341 ms and 683 ms respectively. Those are pretty huge windows when considering measurements in the mid and high frequencies, but necessary to achieve usable LF frequency resolution. The place this clearly shows itself is in the impact that reflected/reverberant energy has on the coherence trace. With a single FFT transfer function, reverb energy arriving 60, 70, 80 ms late has FAR less negative impact than in a multi-time window process that uses significantly shorter TCs for the HF portion of the measurement.

Simply put, the question here is mathematically, what reverberant energy should Smaart consider signal, and what is noise? Here our choice of TC has a significant say - do we want to treat HF the same as LF? Does our listening mechanism? Should our Coh. trace?

We chose, as our default, to use multiple time windows as we had done in the past. So . . . the next question was, what should the TC's be. In the past, we were confined to a short list of "power of 2" FFT/TC sizes. Now here in the future (where I hear everyone is gonna wear 1-piece jump suits) we can easily and efficiently use virtually any TC size. That meant we could choose our TC's with our focus on the resulting frequency resolution and the impact of the TC on our classification of reverberant energy. (What is signal, what is noise?)

Without getting into the exact numbers here (which we have no intention of publishing - but if you are handy with the math, we're confident you can derive the numbers yourself ;) ) we chose the TCs in our new MTW process so that we have >48th octave resolution above 60 Hz, and 1 Hz resolution below 120 Hz. (The math is pretty is pretty easy for figuring that lowest TC :D )

One final note, given the resolution of the new MTW process coupled with our fabulous, new, fractional-octave smoothing algorithms, we no longer combine data points in the HF to create a base 24 FPPO TF resolution. We leave that to your choice of smoothing. (And as always, if you want, you can still go back to single FFT transfer function if you wish.)

Attached is a screen capture showing FPPO, MTW and single 16k FFT transfer functions so that you can compare resolutions. The MTW and the 16k are of the same measurement. The FPPO is older, unrelated data.

Peas,

-j

Here is a quick discussion of Smaart v7's MTW vs. Smaart v2-6's FPPO, and includes mention of SIM's standard FFT settings for Transfer Function in the mix. (This inclusion is due to the fact that this post began life as a response to a specific question regarding MTW and how it related to SIM's standard FFT settings for Transfer Function measurements.)

FPPO was our previous version (v2 - v6) of using multiple time windows in Transfer Function to create constant (fractional octave) frequency resolution data. FPPO in fact stands for "24 Fixed Points Per Octave." We achieved this though a devious mixture of FFT size and sample rate (via decimation) choices, as well as some data point banding for good measure (where the raw frequency resolution was much greater than the target 24th octave). SIM II uses a similar process (as does SIM III I believe), but generally relies on a more straight forward process that uses more FFT's with simple decimation (1/2'd sample rates) between each.

The factors that drove SIA's decisions when creating the original SmaartPro FPPO process are many - having as much to do with available processor power and data handling issues as with target resolution and TC's. When we began development of v7, we were able to take a fresh look at FPPO and the FFT settings for Transfer Function measurements. With processor power being what it is today, running FFT's of 16k, 32k or even 64k in real-time was no longer a concern. So we had to ask ourselves, do we need/want to use a multiple FFT based approach? Why not just run a huge FFT and smooth it to whatever target fractional octave resolution we wish?

Our answer for the first question was, yes, we still want to use multiple FFT's as our default. And the reason we do was the answer to the second question. (Here is the quick version) Single 16k and 32k FFTs have measurement TCs (time constants) of 341 ms and 683 ms respectively. Those are pretty huge windows when considering measurements in the mid and high frequencies, but necessary to achieve usable LF frequency resolution. The place this clearly shows itself is in the impact that reflected/reverberant energy has on the coherence trace. With a single FFT transfer function, reverb energy arriving 60, 70, 80 ms late has FAR less negative impact than in a multi-time window process that uses significantly shorter TCs for the HF portion of the measurement.

Simply put, the question here is mathematically, what reverberant energy should Smaart consider signal, and what is noise? Here our choice of TC has a significant say - do we want to treat HF the same as LF? Does our listening mechanism? Should our Coh. trace?

We chose, as our default, to use multiple time windows as we had done in the past. So . . . the next question was, what should the TC's be. In the past, we were confined to a short list of "power of 2" FFT/TC sizes. Now here in the future (where I hear everyone is gonna wear 1-piece jump suits) we can easily and efficiently use virtually any TC size. That meant we could choose our TC's with our focus on the resulting frequency resolution and the impact of the TC on our classification of reverberant energy. (What is signal, what is noise?)

Without getting into the exact numbers here (which we have no intention of publishing - but if you are handy with the math, we're confident you can derive the numbers yourself ;) ) we chose the TCs in our new MTW process so that we have >48th octave resolution above 60 Hz, and 1 Hz resolution below 120 Hz. (The math is pretty is pretty easy for figuring that lowest TC :D )

One final note, given the resolution of the new MTW process coupled with our fabulous, new, fractional-octave smoothing algorithms, we no longer combine data points in the HF to create a base 24 FPPO TF resolution. We leave that to your choice of smoothing. (And as always, if you want, you can still go back to single FFT transfer function if you wish.)

Attached is a screen capture showing FPPO, MTW and single 16k FFT transfer functions so that you can compare resolutions. The MTW and the 16k are of the same measurement. The FPPO is older, unrelated data.

Peas,

-j