Ka Nānā ʻana i ka Alapine (Frequency Spectrum)
He ʻano koʻikoʻi ka nānā ʻana i ka alapine (frequency spectrum) i ka ʻenekinia hōʻailona a me ke kamaʻilio ʻana, i hoʻohana ʻia e aʻo i ka hoʻolaha alapine o kahi hōʻailona. He ʻano hana koʻikoʻi ia no ka hoʻomaopopo ʻana i nā ʻano paʻakikī o nā hōʻailona ma ke kahua alapine. Ma kēia ʻatikala, e kūkākūkā kikoʻī mākou i nā manaʻo kumu, nā ʻano loiloi, nā noi, a me nā pilikia i kū i ka nānā ʻana i ka alapine.
Nā Manaʻo Kumu
ʻO ke alapine (frequency) ka helu o nā pōʻaiapuni i kekona o kahi nalu sine. Hiki ke hoʻokaʻawale ʻia kahi hōʻailona i nā ʻāpana sinusoidal me nā alapine (frequencies) a me nā amplitudes kikoʻī. Ua ʻike ʻia kēia haki ʻana he moʻo Fourier a i ʻole ka hoʻololi Fourier no kahi hōʻailona hoʻomau.
Hoʻololi Fourier
Hoʻololi ka hoʻololi Fourier i kahi hōʻailona mai ka ʻāpana manawa i ka ʻāpana alapine. Inā he hōʻailona ʻo \( x(t) \) ma ka ʻāpana manawa, a laila ua hōʻike ʻia ka hoʻololi Fourier \( X(f) \) penei:
\[
Ma hea:
– ʻO \( j \) ke anakahi hoʻokalakupua (\(\sqrt{-1}\)),
– ʻo \( f \) ke alapine (frequency),
– ʻO ka manawa ka \( t \).
Hāʻawi kēia hoʻololi ʻana i ka alapine (frequency spectrum) o ka hōʻailona mua, ʻo ia hoʻi, ka ʻike e pili ana i nā amplitudes a me nā pae o nā ʻāpana alapine like ʻole i loko o ka hōʻailona.
Alapine (Frequency Spectrum)
ʻO ka alapine (frequency spectrum) he hōʻike ia o kahi hōʻailona ma ke kikowaena alapine, e hōʻike ana i ka amplitude (a i ʻole ka ikaika) o kēlā me kēia ʻāpana alapine. ʻElua mau ʻāpana koʻikoʻi i loko o kahi alapine:
1. Ka nui o ke kiʻikuhi: Hōʻike i ka amplitude o kēlā me kēia ʻāpana alapine (frequency).
2. Pae Kiʻi: Hōʻike i ke pae o kēlā me kēia ʻāpana alapine (frequency).
ʻAno loiloi
Aia nā ʻano hana like ʻole i hoʻohana ʻia i ka nānā ʻana i ka alapine (frequency spectrum). ʻO kekahi o nā mea maʻamau:
1. Hoʻololi Fourier Discrete (DFT) a me ka Hoʻololi Fourier wikiwiki (FFT)
He ʻano hana kumu ka DFT i hoʻohana ʻia e kālailai i ke alapine (frequency spectrum) o ka ʻikepili diskrit. Ma muli o ka hiki ke hoʻopau manawa i nā helu ʻana o DFT, hoʻohana pinepine ʻia ka FFT ma ke ʻano he mana ʻoi aku ka maikaʻi o ka DFT.
2. Ka Nānā ʻana i ka Puka makani
No nā hōʻailona paʻa ʻole, kahi e loli ai nā ʻano alapine (frequency) i ka hala ʻana o ka manawa, ua māhele ʻia ka hōʻailona i nā ʻāpana pōkole, a laila ua hoʻopili ʻia ka FFT i kēlā me kēia ʻāpana. Ua ʻike ʻia kēia ʻano hana ʻo ka Short-Time Fourier Transform (STFT).
3. Hoʻololi Nalu
ʻO ka hoʻololi wavelet kahi ʻenehana i hoʻolālā ʻia no ka nānā ʻana i nā hōʻailona paʻa ʻole. ʻAʻole e like me ka FFT, hiki i ka hoʻololi wavelet ke hāʻawi i ka hoʻonā ma nā ʻāpana alapine a me ka manawa.
4. Ka Nānā ʻana o ka Cepstrum Spectral
ʻO ka cepstrum kahi hoʻololi logarithmic o ka nui o ka spectrum alapine (frequency spectrum) i loko o ke kikowaena manawa. Hoʻohana ʻia ia e ʻike i nā leo a i ʻole nā periodicities i loko o kahi hōʻailona.
Noi Loiloi Alapine (Frequency Spectrum Analysis)
He nui nā noi o ka loiloi alapine (frequency spectrum analysis) ma nā ʻano like ʻole, e like me:
1. Kelepona
I nā ʻōnaehana kamaʻilio, hoʻohana ʻia ka nānā ʻana o ka spectrum e ʻike i nā kumu hoʻopilikia alapine (frequency interference), hoʻolālā i nā kānana, a hoʻonui i ka bandwidth.
2. Leo a me ke Mele
I loko o ka hana ʻana i nā hōʻailona I ke kani, hoʻohana ʻia ka nānā ʻana o ka alapine (frequency spectrum) e ʻike i ka pitch, e hoʻomaopopo i ke kuʻikahi, a kālailai i ka timbre o nā mea kani like ʻole.
3. Lapaʻau
I loko o kahua lapaʻau, hoʻohana ʻia ke alapine (frequency spectrum) i ka nānā ʻana i nā hōʻailona EEG (electroencephalogram) a me ECG (electrocardiogram) no ka ʻike ʻana i ka maʻi.
4. Seismology
Hoʻohana ʻia ke alapine (frequency spectrum) e aʻo i nā ōlaʻi a me nā hana seismic e hāʻawi i ka ʻike hohonu i nā hanana geophysical.
5. Radar a me Sonar
Kōkua ka nānā ʻana o ka alapine (frequency spectrum) i ka radar a me ka sonar i ka ʻike ʻana i nā mea e pili ana i ka hoʻākāka ʻana o nā nalu electromagnetic a me nā nalu kani.
Tantangan
ʻOiai kona koʻikoʻi, ʻaʻole pilikia ka nānā ʻana i ka alapine (frequency spectrum):
1. Hoʻonā pinepine vs. Manawa
Aia kahi kūkaʻi ma waena o ka hoʻonā manawa a me ka hoʻonā alapine (frequency). ʻO STFTs, no ka laʻana, hāʻawi i ka hōʻike maikaʻi akā ua kaupalena ʻia e ka hoʻonā hiki iā lākou ke hoʻokō no nā hōʻailona e loli wikiwiki ana.
2. Walaʻau a me ka hewa
Hiki i nā hōʻailona me ka walaʻau ke uhi i ka alapine (frequency spectrum). Hoʻohana pinepine ʻia nā ʻano kānana a me ka awelika, akā ʻo ka hoʻokaʻawale ʻana i ka hōʻailona mai ka walaʻau he mea paʻakikī mau ia ma lalo o kekahi mau kūlana.
3. Ka helu ʻana a me ka ʻikepili
No ka ʻikepili nui a me nā hōʻailona hoʻonā kiʻekiʻe, pono ka nānā ʻana o ka alapine (frequency spectrum) i ka helu ʻana a me ka hiki ke mālama nui. kumuwaiwai lilo ka helu ʻana i mea nui.
Ka hopena
He mea hana ikaika ka loiloi alapine (frequency spectrum) i ka hana hōʻailona a me ke kamaʻilio ʻana. Hāʻawi ia i nā ʻike hohonu i nā ʻāpana alapine o nā hōʻailona i loaʻa ʻole i ka manawa. Me nā noi mai ke kelepona a hiki i ka lāʻau lapaʻau, he kuleana koʻikoʻi kēia loiloi i ka ʻenehana hou. Eia nō naʻe, ʻo kona hoʻohana pono ʻana e pono ai ka hoʻomaopopo piha ʻana i ke ʻano hana, nā pilikia i kū i mua, a me nā kaʻina hana wikiwiki kūpono. I ka holomua ʻana o ka ʻenehana a me nā ʻano loiloi e holomua ana, hiki iā mākou ke manaʻo i nā hoʻomaikaʻi hou aʻe i ka nānā ʻana a me ka hoʻopili ʻana i ka alapine (frequency spectrum) ma nā ʻano like ʻole.
