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Pending Acquisition - Additional Information (Detail) - USD ($) $ / shares in Units, $ in Millions | 3 Months Ended |
--- | --- | ---
Sep. 25, 2021 | Aug. 30, 2021
Senior Credit Facility [Member] |  |
Business Acquisition [Line Items] |  |
Incremental debt financing |  | $ 600.0
DSPG [Member] |  |
Business Acquisition [Line Items] |  |
Date of acquisition agreement | Aug. 30, 2021 |
Business acquisition price per share issued and outstanding | $ 22.00 |

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- Definition Incremental debt financing. + References No definition available. + Details
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Namespace Prefix: | syna_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition Date when the business acquisition agreement was executed, in YYYY-MM-DD format. + References No definition available. + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:dateItemType
Balance Type: | na
Period Type: | duration

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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition Price of a single share of a number of saleable stocks paid or offered to be paid in a business combination. + References No definition available. + Details
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Namespace Prefix: | us-gaap_
Data Type: | dtr-types:perShareItemType
Balance Type: | na
Period Type: | instant

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- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_BusinessAcquisitionAxis=syna_DspGroupIncMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |