{"id":686,"date":"2013-12-15T14:13:24","date_gmt":"2013-12-15T21:13:24","guid":{"rendered":"https:\/\/inkofpark.wordpress.com\/?p=686"},"modified":"2024-09-01T20:07:12","modified_gmt":"2024-09-02T02:07:12","slug":"candle-flame-flicker","status":"publish","type":"post","link":"https:\/\/www.inkofpark.com\/?p=686","title":{"rendered":"Candle Flame Flicker"},"content":{"rendered":"

For a project I wanted to make an LED flicker like a candle. I searched for the signal statistics of candle flicker, and I found no data. One student web site<\/a> suggests that candle flame flicker is a 1\/f<\/em>-type random signal with roll-off of 20 dB per decade increase in frequency. Similar processes are typical for turbulence, so this student\u2019s plan seemed reasonable. However, the student did not discuss whether the signal is Gaussian or not, and did not describe the low-frequency characteristics of the signal. 1\/f<\/em> noises may have a spectrum that follows the 1\/f curve to very low frequencies, but because they would require infinite power at f<\/em>=0 they always have some lower frequency change. I had no data.<\/p>\n

Candles aren\u2019t hard to get, and I already had a silicon photodiode for an absorptive smoke density measurement system I\u2019m working on. I also had an analog-to-digital converter (ADC) in an ADS1015 on a breakout board from Adafruit. I made the very simple circuit shown below and attached it to a Raspberry Pi to sample the data. There are a lot more details, but those are later.<\/p>\n

\"circuit\"<\/a><\/p>\n

The voltage measured by the ADC is directly proportional to the current through the resistor. The current through the reverse-biased diode is directly proportional to the incident optical power. Very simple. I recorded a minute of data at a low 250 Hz sample rate, and subjected the data to analysis. The setup was a nominally dark room with the sensor a few inches from the flame. I flapped my hand at the candle to get it to flicker while recording.<\/p>\n

\"20131211-04\"<\/a><\/p>\n

\"20131211-06\"<\/a><\/p>\n

\"20131211-12\"<\/a><\/p>\n

The first graph below is a histogram of sample values.<\/p>\n

\"dfile_hist\"<\/a><\/p>\n

The histogram is about normally distributed, but the right-hand tail is not Gaussian; it is too fat. In other words the candle is occasionally much brighter than normal. The time series (below) shows the same properties. There are clearly visible large excursions.<\/p>\n

\"dfile_time\"<\/a><\/p>\n

For human eyes the candle\u2019s flicker will be well represented if the frequency spectrum of the flicker and the distribution of the flicker approximately match a natural source. The spectrum below can be thought of as an average brightness (the peak at the left), a flat spectral region out to about 4 Hz, and then a 1\/f<\/em>-style roll off at 44 dB per decade.<\/p>\n

\"dfile_psd\"<\/a><\/p>\n

Numerically, we have the recipe for a flickering candle:<\/p>\n