So, as I learned during my recordings, church acoustics apply just as much to the heating system as it does to choirs and organs, which means that I have to put the actual creation of my sample patches off, and focus on getting as clean a signal as possible without reducing the fidelity of the organ. Which leads me to look into the process of noise reduction.
I’m going to preface this by saying, I don’t fully understand this process, these algorithms, or half of what I’m going to be trying to talk about in this post.
So, the process of noise reduction can be done in many different ways, but the first thing to understand is the two types of noise reduction algorithms: Fixed and Adaptive.
Fixed Noise Reduction
Fixed noise reduction, or spectral noise gating uses Fourier analysis of sample sections of noise to create a spectrum graph, which is used to gate the audio, reducing the level for any sound that isn’t about the threshold. This threshold varies at different frequency bands in order to sufficiently remove the background sound during sections that are above the threshold.
XNoise – Waves Plugin
This works best for samples which have a consistent noise throughout the entire sample, as the filter is static.
This gating is often combined with other processes such as frequency smoothing and time smoothing, which both are baffling to me for the time being. From what I can gather, these processes help to make it so that the effects of the noise gating don’t degrade the quality of the frequencies that are above the threshold at any given time, but again, I’m still not 100% on what they are or what they do, and definitely not how they work. 
Adaptive Noise Reduction
Adaptive filtering is a process which models the relationship between the input and output of a filter throughout the duration of it’s use. This means that it adjusts, or adapts, to the changing signal and as such, adaptive noise reduction is typically used for samples with noise that varies over the duration of the recording.
where x(n) is the input signal to a linear filter
y(n) is the corresponding output signal
d(n) is an additional input signal to the adaptive filter
e(n) is the error signal that denotes the difference between d(n) and y(n). 
The process is similar to fixed reduction, but instead of using a Fourier analysis of the noise, the filter is created with a Least Mean Square algorithm. This takes a fixed filter like the Fourier example used above and changes the variables of the filter (ie. the threshold in each frequency band) in response to the input signal.
The quality of both of these types of filtering depend on the specific algorithm used. And quality noise reduction software isn’t cheap. Waves noise reduction plugins range between $200 and $600, iZotope’s RX3 runs $1200 for a full version copy, and CEDAR’s noise reduction hardware units (like the DNS1500) run upwards of $5000.
And it makes sense, in a world where audio is often second (or third) fiddle, it’s not always possible to get the best recordings, so noise reduction is a necessity.
- Advanced Digital Signal Processing and Noise Reduction, Second Edition. Chapter 11 – Saeed V. Vaseghi
- Noise Reduction Based on Modified Spectral Subtraction Method – Ekaterina Verteletskaya, Boris Simak
- Digital Signal Processing Algorithms for Noise Reduction, Dynamic Range Compression, and Feedback Cancellation in Hearing Aids – Kim Ngo
- Least Mean Square (LMS) Adaptive Filtering – National Instruments